5 4factoring trinomial ii
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Factoring Trinomials II
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c.
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods.
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable.
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable. The second one takes more steps but gives definite answers.
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable. The second one takes more steps but gives definite answers. Reversed FOIL Method
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable. The second one takes more steps but gives definite answers. For this method, we need to find four numbers that fit certain descriptions.
Reversed FOIL Method
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable. The second one takes more steps but gives definite answers. For this method, we need to find four numbers that fit certain descriptions. The following are examples of the task to be accomplished.
Reversed FOIL Method
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable. The second one takes more steps but gives definite answers. For this method, we need to find four numbers that fit certain descriptions. The following are examples of the task to be accomplished. Example A. Let {1, 3} and {1, 2} be two pairs of numbers. Is it possible to split the {1, 2 }, put them in the boxes that makes the equality true?
Reversed FOIL Method
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable. The second one takes more steps but gives definite answers. For this method, we need to find four numbers that fit certain descriptions. The following are examples of the task to be accomplished. Example A. Let {1, 3} and {1, 2} be two pairs of numbers. Is it possible to split the {1, 2 }, put them in the boxes that makes the equality true?
a. 1* (± ) + 3*(± ) = 5.
Reversed FOIL Method
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable. The second one takes more steps but gives definite answers. For this method, we need to find four numbers that fit certain descriptions. The following are examples of the task to be accomplished. Example A. Let {1, 3} and {1, 2} be two pairs of numbers. Is it possible to split the {1, 2 }, put them in the boxes that makes the equality true?
a. 1* (± ) + 3*(± ) = 5.
Yes, 1* (2) + 3 * (1) = 5
Reversed FOIL Method
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable. The second one takes more steps but gives definite answers. For this method, we need to find four numbers that fit certain descriptions. The following are examples of the task to be accomplished. Example A. Let {1, 3} and {1, 2} be two pairs of numbers. Is it possible to split the {1, 2 }, put them in the boxes that makes the equality true?
a. 1* (± ) + 3*(± ) = 5.
Yes, 1* (2) + 3 * (1) = 5
b. 1* (± ) + 3* (± ) = –5.
Reversed FOIL Method
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable. The second one takes more steps but gives definite answers. For this method, we need to find four numbers that fit certain descriptions. The following are examples of the task to be accomplished. Example A. Let {1, 3} and {1, 2} be two pairs of numbers. Is it possible to split the {1, 2 }, put them in the boxes that makes the equality true?
a. 1* (± ) + 3*(± ) = 5.
Yes, 1* (2) + 3 * (1) = 5
b. 1* (± ) + 3* (± ) = –5.Yes, 1* (1) + 3* (–2) = –5
Reversed FOIL Method
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable. The second one takes more steps but gives definite answers. For this method, we need to find four numbers that fit certain descriptions. The following are examples of the task to be accomplished. Example A. Let {1, 3} and {1, 2} be two pairs of numbers. Is it possible to split the {1, 2 }, put them in the boxes that makes the equality true?
a. 1* (± ) + 3*(± ) = 5.
Yes, 1* (2) + 3 * (1) = 5
b. 1* (± ) + 3* (± ) = –5.Yes, 1* (1) + 3* (–2) = –5 or 1* (–2) + 3* (–1) = –5
Reversed FOIL Method
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable. The second one takes more steps but gives definite answers. For this method, we need to find four numbers that fit certain descriptions. The following are examples of the task to be accomplished. Example A. Let {1, 3} and {1, 2} be two pairs of numbers. Is it possible to split the {1, 2 }, put them in the boxes that makes the equality true?
a. 1* (± ) + 3*(± ) = 5.
Yes, 1* (2) + 3 * (1) = 5
b. 1* (± ) + 3* (± ) = –5.Yes, 1* (1) + 3* (–2) = –5 or 1* (–2) + 3* (–1) = –5
c. 1* (± ) + 3* (± ) = 8.
Reversed FOIL Method
Factoring Trinomials IINow let’s try to factor trinomials of the form ax2 + bx + c. We’ll give two methods. One is short but not reliable. The second one takes more steps but gives definite answers. For this method, we need to find four numbers that fit certain descriptions. The following are examples of the task to be accomplished. Example A. Let {1, 3} and {1, 2} be two pairs of numbers. Is it possible to split the {1, 2 }, put them in the boxes that makes the equality true?
a. 1* (± ) + 3*(± ) = 5.
Yes, 1* (2) + 3 * (1) = 5
b. 1* (± ) + 3* (± ) = –5.Yes, 1* (1) + 3* (–2) = –5 or 1* (–2) + 3* (–1) = –5
c. 1* (± ) + 3* (± ) = 8.No, since the most we can obtain is 1* (1) + 3* (2) = 7.
Reversed FOIL Method
Factoring Trinomials II(Reversed FOIL Method)
Factoring Trinomials II(Reversed FOIL Method) Let’s see how the above examples are related to factoring.
Example B. Factor 3x2 + 5x + 2.
Factoring Trinomials II(Reversed FOIL Method) Let’s see how the above examples are related to factoring.
Example B. Factor 3x2 + 5x + 2.
The only way to get 3x2 is (3x ± #)(1x ± #).
Factoring Trinomials II(Reversed FOIL Method) Let’s see how the above examples are related to factoring.
Example B. Factor 3x2 + 5x + 2.
The only way to get 3x2 is (3x ± #)(1x ± #).
The #’s must be 1 and 2 to get the constant term +2.
Factoring Trinomials II(Reversed FOIL Method) Let’s see how the above examples are related to factoring.
Example B. Factor 3x2 + 5x + 2.
The only way to get 3x2 is (3x ± #)(1x ± #).
The #’s must be 1 and 2 to get the constant term +2.
We need to place 1 and 2 as the #'s so the product will yield the correct middle term +5x.
Factoring Trinomials II(Reversed FOIL Method) Let’s see how the above examples are related to factoring.
Example B. Factor 3x2 + 5x + 2.
The only way to get 3x2 is (3x ± #)(1x ± #).
The #’s must be 1 and 2 to get the constant term +2.
We need to place 1 and 2 as the #'s so the product will yield the correct middle term +5x.
That is, (3x ± #)(1x ± #) must yields +5x,
Factoring Trinomials II(Reversed FOIL Method) Let’s see how the above examples are related to factoring.
3(± # ) +1(± #) = 5 where the #’s are 1 and 2.
Factoring Trinomials II(Reversed FOIL Method) Let’s see how the above examples are related to factoring.
Example B. Factor 3x2 + 5x + 2.
The only way to get 3x2 is (3x ± #)(1x ± #).
The #’s must be 1 and 2 to get the constant term +2.
We need to place 1 and 2 as the #'s so the product will yield the correct middle term +5x.
That is, (3x ± #)(1x ± #) must yields +5x, or that
3(± # ) +1(± #) = 5 where the #’s are 1 and 2.
Since 3(1) +1(2) = 5,
Factoring Trinomials II(Reversed FOIL Method) Let’s see how the above examples are related to factoring.
Example B. Factor 3x2 + 5x + 2.
The only way to get 3x2 is (3x ± #)(1x ± #).
The #’s must be 1 and 2 to get the constant term +2.
We need to place 1 and 2 as the #'s so the product will yield the correct middle term +5x.
That is, (3x ± #)(1x ± #) must yields +5x, or that
3(± # ) +1(± #) = 5 where the #’s are 1 and 2.
Since 3(1) +1(2) = 5, we see that
3x2 + 5x + 2 = (3x + 2)(1x + 1).
Factoring Trinomials II(Reversed FOIL Method) Let’s see how the above examples are related to factoring.
Example B. Factor 3x2 + 5x + 2.
The only way to get 3x2 is (3x ± #)(1x ± #).
The #’s must be 1 and 2 to get the constant term +2.
We need to place 1 and 2 as the #'s so the product will yield the correct middle term +5x.
That is, (3x ± #)(1x ± #) must yields +5x, or that
3(± # ) +1(± #) = 5 where the #’s are 1 and 2.
Since 3(1) +1(2) = 5, we see that
3x2 + 5x + 2 = (3x + 2)(1x + 1).5x
Factoring Trinomials II(Reversed FOIL Method) Let’s see how the above examples are related to factoring.
Example B. Factor 3x2 + 5x + 2.
The only way to get 3x2 is (3x ± #)(1x ± #).
The #’s must be 1 and 2 to get the constant term +2.
We need to place 1 and 2 as the #'s so the product will yield the correct middle term +5x.
That is, (3x ± #)(1x ± #) must yields +5x, or that
Factoring Trinomials IIExample C. Factor 3x2 – 7x + 2.
Factoring Trinomials IIExample C. Factor 3x2 – 7x + 2.
We start with (3x ± #)(1x ± #).
3(± # ) + 1(± # ) = –7.
Factoring Trinomials IIExample C. Factor 3x2 – 7x + 2.
We start with (3x ± #)(1x ± #). We need to fill in 1 and 2 as #'s so that
3(± # ) + 1(± # ) = –7.It's 3(–2) + 1(–1) = –7.
Factoring Trinomials IIExample C. Factor 3x2 – 7x + 2.
We start with (3x ± #)(1x ± #). We need to fill in 1 and 2 as #'s so that
3(± # ) + 1(± # ) = –7.It's 3(–2) + 1(–1) = –7.So 3x2 – 7x + 2 = (3x –1)(1x – 2)
Factoring Trinomials IIExample C. Factor 3x2 – 7x + 2.
We start with (3x ± #)(1x ± #). We need to fill in 1 and 2 as #'s so that
3(± # ) + 1(± # ) = –7.It's 3(–2) + 1(–1) = –7.So 3x2 – 7x + 2 = (3x –1)(1x – 2)
Example D. Factor 3x2 + 5x – 2.
Factoring Trinomials IIExample C. Factor 3x2 – 7x + 2.
We start with (3x ± #)(1x ± #). We need to fill in 1 and 2 as #'s so that
3(± # ) + 1(± # ) = –7.It's 3(–2) + 1(–1) = –7.So 3x2 – 7x + 2 = (3x –1)(1x – 2)
Example D. Factor 3x2 + 5x – 2.
We start with (3x ± #)(1x ± #).
Factoring Trinomials IIExample C. Factor 3x2 – 7x + 2.
We start with (3x ± #)(1x ± #). We need to fill in 1 and 2 as #'s so that
3(± # ) + 1(± # ) = –7.It's 3(–2) + 1(–1) = –7.So 3x2 – 7x + 2 = (3x –1)(1x – 2)
Example D. Factor 3x2 + 5x – 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1 and 2 so that
3(± # ) + 1(± # ) = +5.
Factoring Trinomials IIExample C. Factor 3x2 – 7x + 2.
We start with (3x ± #)(1x ± #). We need to fill in 1 and 2 as #'s so that
3(± # ) + 1(± # ) = –7.It's 3(–2) + 1(–1) = –7.So 3x2 – 7x + 2 = (3x –1)(1x – 2)
Example D. Factor 3x2 + 5x – 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1 and 2 so that
3(± # ) + 1(± # ) = +5.Since c is negative, they must have opposite signs .
Factoring Trinomials IIExample C. Factor 3x2 – 7x + 2.
We start with (3x ± #)(1x ± #). We need to fill in 1 and 2 as #'s so that
3(± # ) + 1(± # ) = –7.It's 3(–2) + 1(–1) = –7.So 3x2 – 7x + 2 = (3x –1)(1x – 2)
Example D. Factor 3x2 + 5x – 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1 and 2 so that
3(± # ) + 1(± # ) = +5.
It is 3(+2) + 1(–1) = +5.Since c is negative, they must have opposite signs .
Factoring Trinomials IIExample C. Factor 3x2 – 7x + 2.
We start with (3x ± #)(1x ± #). We need to fill in 1 and 2 as #'s so that
3(± # ) + 1(± # ) = –7.It's 3(–2) + 1(–1) = –7.So 3x2 – 7x + 2 = (3x –1)(1x – 2)
Example D. Factor 3x2 + 5x – 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1 and 2 so that
3(± # ) + 1(± # ) = +5.
It is 3(+2) + 1(–1) = +5.So 3x2 + 5x + 2 = (3x –1)(1x + 2)
Since c is negative, they must have opposite signs .
Factoring Trinomials IIExample C. Factor 3x2 – 7x + 2.
We start with (3x ± #)(1x ± #). We need to fill in 1 and 2 as #'s so that
Example E. Factor 3x2 + 8x + 2.
Factoring Trinomials II
Example E. Factor 3x2 + 8x + 2.
We start with (3x ± #)(1x ± #).
Factoring Trinomials II
Example E. Factor 3x2 + 8x + 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1&2 so that
3(± # ) + 1(± # ) = +8.
Factoring Trinomials II
Example E. Factor 3x2 + 8x + 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1&2 so that
3(± # ) + 1(± # ) = +8.This is impossible.
Factoring Trinomials II
Example E. Factor 3x2 + 8x + 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1&2 so that
3(± # ) + 1(± # ) = +8.This is impossible. Hence the expression is prime.
Factoring Trinomials II
Example E. Factor 3x2 + 8x + 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1&2 so that
3(± # ) + 1(± # ) = +8.This is impossible. Hence the expression is prime.
Factoring Trinomials II
If both the numbers a and c in ax2 + bx + c have many factors then there are many possibilities to check.
Example E. Factor 3x2 + 8x + 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1&2 so that
3(± # ) + 1(± # ) = +8.This is impossible. Hence the expression is prime.
Factoring Trinomials II
If both the numbers a and c in ax2 + bx + c have many factors then there are many possibilities to check.
Example F. Factor 3x2 + 11x – 4.
Example E. Factor 3x2 + 8x + 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1&2 so that
3(± # ) + 1(± # ) = +8.This is impossible. Hence the expression is prime.
Factoring Trinomials II
If both the numbers a and c in ax2 + bx + c have many factors then there are many possibilities to check.
Example F. Factor 3x2 + 11x – 4.
We start with (3x ± #)(1x ± #).
Example E. Factor 3x2 + 8x + 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1&2 so that
3(± # ) + 1(± # ) = +8.This is impossible. Hence the expression is prime.
3(± # ) + 1(± # ) = +11.
Factoring Trinomials II
If both the numbers a and c in ax2 + bx + c have many factors then there are many possibilities to check.
Example F. Factor 3x2 + 11x – 4.
We start with (3x ± #)(1x ± #). Since 4 = 2(2) = 1(4), we need to fill in 2&2 or 1&4 so that
Example E. Factor 3x2 + 8x + 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1&2 so that
3(± # ) + 1(± # ) = +8.This is impossible. Hence the expression is prime.
3(± # ) + 1(± # ) = +11. It can't be 2&2.
Factoring Trinomials II
If both the numbers a and c in ax2 + bx + c have many factors then there are many possibilities to check.
Example F. Factor 3x2 + 11x – 4.
We start with (3x ± #)(1x ± #). Since 4 = 2(2) = 1(4), we need to fill in 2&2 or 1&4 so that
Example E. Factor 3x2 + 8x + 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1&2 so that
3(± # ) + 1(± # ) = +8.This is impossible. Hence the expression is prime.
3(± # ) + 1(± # ) = +11. It can't be 2&2.
Factoring Trinomials II
If both the numbers a and c in ax2 + bx + c have many factors then there are many possibilities to check.
Example F. Factor 3x2 + 11x – 4.
We start with (3x ± #)(1x ± #). Since 4 = 2(2) = 1(4), we need to fill in 2&2 or 1&4 so that
Try 1&4,
Example E. Factor 3x2 + 8x + 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1&2 so that
3(± # ) + 1(± # ) = +8.This is impossible. Hence the expression is prime.
3(± # ) + 1(± # ) = +11. It can't be 2&2.
Factoring Trinomials II
If both the numbers a and c in ax2 + bx + c have many factors then there are many possibilities to check.
Example F. Factor 3x2 + 11x – 4.
We start with (3x ± #)(1x ± #). Since 4 = 2(2) = 1(4), we need to fill in 2&2 or 1&4 so that
Try 1&4, it is 3(+4) + 1(–1) = +11.
Example E. Factor 3x2 + 8x + 2.
We start with (3x ± #)(1x ± #).
We need to fill in 1&2 so that
3(± # ) + 1(± # ) = +8.This is impossible. Hence the expression is prime.
3(± # ) + 1(± # ) = +11. It can't be 2&2.
Factoring Trinomials II
If both the numbers a and c in ax2 + bx + c have many factors then there are many possibilities to check.
Example F. Factor 3x2 + 11x – 4.
We start with (3x ± #)(1x ± #). Since 4 = 2(2) = 1(4), we need to fill in 2&2 or 1&4 so that
Try 1&4, it is 3(+4) + 1(–1) = +11. So 3x2 + 11x – 4 = (3x – 1)(1x + 4).
Factoring Trinomials IIIt's not necessary to always start with ax2. If c is a prime number, we start with c.
Example G. Factor 12x2 – 5x – 3.
Factoring Trinomials IIIt's not necessary to always start with ax2. If c is a prime number, we start with c.
Example G. Factor 12x2 – 5x – 3.
Since 3 must be 3(1),
Factoring Trinomials IIIt's not necessary to always start with ax2. If c is a prime number, we start with c.
Example G. Factor 12x2 – 5x – 3.
Since 3 must be 3(1), we need to find two numbers such that (#)(#) = 12
Factoring Trinomials IIIt's not necessary to always start with ax2. If c is a prime number, we start with c.
Example G. Factor 12x2 – 5x – 3.
Since 3 must be 3(1), we need to find two numbers such that (#)(#) = 12 and that
Factoring Trinomials IIIt's not necessary to always start with ax2. If c is a prime number, we start with c.
(± #)(± 3) + (± #)(±1) = – 5.
Example G. Factor 12x2 – 5x – 3.
Since 3 must be 3(1), we need to find two numbers such that (#)(#) = 12 and that
Factoring Trinomials IIIt's not necessary to always start with ax2. If c is a prime number, we start with c.
(± #)(± 3) + (± #)(±1) = – 5. 12 = 1(12) = 2(6) = 3(4)
Example G. Factor 12x2 – 5x – 3.
Since 3 must be 3(1), we need to find two numbers such that (#)(#) = 12 and that
Factoring Trinomials IIIt's not necessary to always start with ax2. If c is a prime number, we start with c.
(± #)(± 3) + (± #)(±1) = – 5. 12 = 1(12) = 2(6) = 3(4) 1&12 and 2&6 can be quickly eliminated.
Example G. Factor 12x2 – 5x – 3.
Since 3 must be 3(1), we need to find two numbers such that (#)(#) = 12 and that
Factoring Trinomials IIIt's not necessary to always start with ax2. If c is a prime number, we start with c.
(± #)(± 3) + (± #)(±1) = – 5. 12 = 1(12) = 2(6) = 3(4) 1&12 and 2&6 can be quickly eliminated. We get (3)(–3) + (4)(+1) = – 5.
Example G. Factor 12x2 – 5x – 3.
Since 3 must be 3(1), we need to find two numbers such that (#)(#) = 12 and that
So 12x2 – 5x – 3 = (3x + 1)(4x – 3).
Factoring Trinomials IIIt's not necessary to always start with ax2. If c is a prime number, we start with c.
(± #)(± 3) + (± #)(±1) = – 5. 12 = 1(12) = 2(6) = 3(4) 1&12 and 2&6 can be quickly eliminated. We get (3)(–3) + (4)(+1) = – 5.
Example G. Factor 12x2 – 5x – 3.
Since 3 must be 3(1), we need to find two numbers such that (#)(#) = 12 and that
So 12x2 – 5x – 3 = (3x + 1)(4x – 3).
Factoring Trinomials IIIt's not necessary to always start with ax2. If c is a prime number, we start with c.
(± #)(± 3) + (± #)(±1) = – 5. 12 = 1(12) = 2(6) = 3(4) 1&12 and 2&6 can be quickly eliminated. We get (3)(–3) + (4)(+1) = – 5.
Remark:In the above method, finding(#)(± #) + (#)( ± #) = b does not guarantee that the trinomial will factor.
Example G. Factor 12x2 – 5x – 3.
Since 3 must be 3(1), we need to find two numbers such that (#)(#) = 12 and that
So 12x2 – 5x – 3 = (3x + 1)(4x – 3).
Factoring Trinomials IIIt's not necessary to always start with ax2. If c is a prime number, we start with c.
(± #)(± 3) + (± #)(±1) = – 5. 12 = 1(12) = 2(6) = 3(4) 1&12 and 2&6 can be quickly eliminated. We get (3)(–3) + (4)(+1) = – 5.
Remark:In the above method, finding(#)(± #) + (#)( ± #) = b does not guarantee that the trinomial will factor. We have to match the sign of c also.
Example H. Factor 3x2 – 7x – 2 .
Factoring Trinomials II
Example H. Factor 3x2 – 7x – 2 .
We start with (3x ± #)(1x ± #).
Factoring Trinomials II
Example H. Factor 3x2 – 7x – 2 .
We start with (3x ± #)(1x ± #). We find that:
3(–2) + 1(–1) = –7.
Factoring Trinomials II
Example H. Factor 3x2 – 7x – 2 .
We start with (3x ± #)(1x ± #). We find that:
3(–2) + 1(–1) = –7.But this won't work since (–2)(–1) = 2 = c.
Factoring Trinomials II
Example H. Factor 3x2 – 7x – 2 .
We start with (3x ± #)(1x ± #). We find that:
3(–2) + 1(–1) = –7.But this won't work since (–2)(–1) = 2 = c. In fact this trinomial is prime.
Factoring Trinomials II
Example H. Factor 3x2 – 7x – 2 .
We start with (3x ± #)(1x ± #). We find that:
3(–2) + 1(–1) = –7.But this won't work since (–2)(–1) = 2 = c. In fact this trinomial is prime.
Factoring Trinomials II
There might be multiple matchings for(#)(± #) + (#)( ± #) = b make sure you chose the correct one, if any.
Example H. Factor 3x2 – 7x – 2 .
We start with (3x ± #)(1x ± #). We find that:
3(–2) + 1(–1) = –7.But this won't work since (–2)(–1) = 2 = c. In fact this trinomial is prime.
Factoring Trinomials II
Example I: Factor 1x2 + 5x – 6 .
There might be multiple matchings for(#)(± #) + (#)( ± #) = b make sure you chose the correct one, if any.
Example H. Factor 3x2 – 7x – 2 .
We start with (3x ± #)(1x ± #). We find that:
3(–2) + 1(–1) = –7.But this won't work since (–2)(–1) = 2 = c. In fact this trinomial is prime.
Factoring Trinomials II
Example I: Factor 1x2 + 5x – 6 .
We have:1(+3) + 1(+2) = +5
There might be multiple matchings for(#)(± #) + (#)( ± #) = b make sure you chose the correct one, if any.
Example H. Factor 3x2 – 7x – 2 .
We start with (3x ± #)(1x ± #). We find that:
3(–2) + 1(–1) = –7.But this won't work since (–2)(–1) = 2 = c. In fact this trinomial is prime.
Factoring Trinomials II
Example I: Factor 1x2 + 5x – 6 .
We have:1(+3) + 1(+2) = +5 1(+6) + 1(–1) = +5
There might be multiple matchings for(#)(± #) + (#)( ± #) = b make sure you chose the correct one, if any.
Example H. Factor 3x2 – 7x – 2 .
We start with (3x ± #)(1x ± #). We find that:
3(–2) + 1(–1) = –7.But this won't work since (–2)(–1) = 2 = c. In fact this trinomial is prime.
Factoring Trinomials II
Example I: Factor 1x2 + 5x – 6 .
We have:1(+3) + 1(+2) = +5
The one that works is x2 + 5x – 6 = (x + 6)(x – 1).
1(+6) + 1(–1) = +5
There might be multiple matchings for(#)(± #) + (#)( ± #) = b make sure you chose the correct one, if any.
Factoring Trinomials IIFinally, before starting the reverse-FOIL procedure
Factoring Trinomials IIFinally, before starting the reverse-FOIL procedure1. make sure the terms are arranged in order.
Factoring Trinomials IIFinally, before starting the reverse-FOIL procedure1. make sure the terms are arranged in order. 2. if there is any common factor, pull out the GCF first.
Factoring Trinomials IIFinally, before starting the reverse-FOIL procedure1. make sure the terms are arranged in order. 2. if there is any common factor, pull out the GCF first. 3. make sure that x2 is positive, if not, factor out the negative sign first.
Factoring Trinomials IIFinally, before starting the reverse-FOIL procedure1. make sure the terms are arranged in order. 2. if there is any common factor, pull out the GCF first. 3. make sure that x2 is positive, if not, factor out the negative sign first.
Example J. Factor –x3 + 3x + 2x2
Factoring Trinomials IIFinally, before starting the reverse-FOIL procedure1. make sure the terms are arranged in order. 2. if there is any common factor, pull out the GCF first. 3. make sure that x2 is positive, if not, factor out the negative sign first.
Example J. Factor –x3 + 3x + 2x2
–x3 + 3x + 2x2 Arrange the terms in order
= –x3 + 2x2 + 3x
Factoring Trinomials IIFinally, before starting the reverse-FOIL procedure1. make sure the terms are arranged in order. 2. if there is any common factor, pull out the GCF first. 3. make sure that x2 is positive, if not, factor out the negative sign first.
Example J. Factor –x3 + 3x + 2x2
–x3 + 3x + 2x2 Arrange the terms in order
= –x3 + 2x2 + 3x Factor out the GCF
= – x(x2 – 2x – 3)
Factoring Trinomials IIFinally, before starting the reverse-FOIL procedure1. make sure the terms are arranged in order. 2. if there is any common factor, pull out the GCF first. 3. make sure that x2 is positive, if not, factor out the negative sign first.
Example J. Factor –x3 + 3x + 2x2
–x3 + 3x + 2x2 Arrange the terms in order
= –x3 + 2x2 + 3x Factor out the GCF
= – x(x2 – 2x – 3)
= – x(x – 3)(x + 1)
Factoring Trinomials IIFinally, before starting the reverse-FOIL procedure1. make sure the terms are arranged in order. 2. if there is any common factor, pull out the GCF first. 3. make sure that x2 is positive, if not, factor out the negative sign first.
Example J. Factor –x3 + 3x + 2x2
–x3 + 3x + 2x2 Arrange the terms in order
= –x3 + 2x2 + 3x Factor out the GCF
= – x(x2 – 2x – 3)
= – x(x – 3)(x + 1)
Ex. A. Factor the following trinomials. If it’s prime, state so.
1. 3x2 – x – 2 2. 3x2 + x – 2 3. 3x2 – 2x – 14. 3x2 + 2x – 1 5. 2x2 – 3x + 1 6. 2x2 + 3x – 1
8. 2x2 – 3x – 27. 2x2 + 3x – 2
15. 6x2 + 5x – 610. 5x2 + 9x – 2
B. Factor. Factor out the GCF, the “–”, and arrange the terms in order first.
9. 5x2 – 3x – 212. 3x2 – 5x + 211. 3x2 + 5x + 2
14. 6x2 – 5x – 613. 3x2 – 5x + 216. 6x2 – x – 2 17. 6x2 – 13x + 2 18. 6x2 – 13x + 219. 6x2 + 7x + 2 20. 6x2 – 7x + 2
21. 6x2 – 13x + 6
22. 6x2 + 13x + 6 23. 6x2 – 5x – 4 24. 6x2 – 13x + 825. 6x2 – 13x – 8
Factoring Trinomials II
25. 4x2 – 9 26. 4x2 – 4927. 25x2 – 4 28. 4x2 + 9 29. 25x2 + 9
30. – 6x2 – 5xy + 6y2 31. – 3x2 + 2x3– 2x 32. –6x3 – x2 + 2x
33. –15x2 – 25x2 – 10x 34. 12x2y2 –14x2y2 + 4xy2
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