factoring trinomials. warm up multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4....
TRANSCRIPT
![Page 1: Factoring Trinomials. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)](https://reader036.vdocuments.us/reader036/viewer/2022081422/551b85ba550346a10a8b53d7/html5/thumbnails/1.jpg)
Factoring Trinomials
![Page 2: Factoring Trinomials. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)](https://reader036.vdocuments.us/reader036/viewer/2022081422/551b85ba550346a10a8b53d7/html5/thumbnails/2.jpg)
Warm Up
• Multiply:
• 1. (x + 3)(x – 7)
• 2. (x – 6)(x + 5)
• 3. (x + 2)(x + 9)
• 4. (x – 4)(x – 6)
![Page 3: Factoring Trinomials. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)](https://reader036.vdocuments.us/reader036/viewer/2022081422/551b85ba550346a10a8b53d7/html5/thumbnails/3.jpg)
Math 2
• Today’s Question:• How do I factor trinomials with a leading
coefficient of one?
![Page 4: Factoring Trinomials. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)](https://reader036.vdocuments.us/reader036/viewer/2022081422/551b85ba550346a10a8b53d7/html5/thumbnails/4.jpg)
Let’s Multiply
(x+2)(x+1)= x2 + x + 2x + 2= x2 + 3x + 2What if we wanted to “undo” Multiplying?Look at the result that we got above:x2 + 3x + 2How can I write this as a product of binomials?( )( )x x+ +2 1
![Page 5: Factoring Trinomials. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)](https://reader036.vdocuments.us/reader036/viewer/2022081422/551b85ba550346a10a8b53d7/html5/thumbnails/5.jpg)
Ex 1. Factor the TrinomialAlways look for a GCF First!!
• x2 + 4x + 3
( )( )x+ 3 1+x
GCF??... NO!GCF??... NO!
What #s multiply to equal 3?
3 and 1
What multiplies to equal x2
x • x
continued
![Page 6: Factoring Trinomials. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)](https://reader036.vdocuments.us/reader036/viewer/2022081422/551b85ba550346a10a8b53d7/html5/thumbnails/6.jpg)
Ex.1) Continued
(x + 3)(x + 1)
How do I know this is right? Look at the product of the outer and inner terms.Do they add to give you the middle term?YES….so you factored it correctly!
3x + x = 4x
3x
x
![Page 7: Factoring Trinomials. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)](https://reader036.vdocuments.us/reader036/viewer/2022081422/551b85ba550346a10a8b53d7/html5/thumbnails/7.jpg)
Ex.2) Factor the Trinomial
x2 + 5x + 6( )( )
So, do we use 2 and 3 or 1 and 6?Well…which ones will add to give you 5?2 and 3!! Check!3x + 2x = 5x
6
2, 3
1, 6
x2
x, xx+ 2 3+x
2x
3x
GCF??... NO!GCF??... NO!
![Page 8: Factoring Trinomials. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)](https://reader036.vdocuments.us/reader036/viewer/2022081422/551b85ba550346a10a8b53d7/html5/thumbnails/8.jpg)
Ex. 3) Factor the Trinomial
x2 – 2x – 3
( )( ) -3 x2
-3, 1
-1, 3
x, xx- 3 1+x
So, do we use -3 and 1 or -1 and 3?Well…which ones will add to give you -2?-3 and 1!! Check!x + -3x = -2x
-3x
x
GCF??... NO!GCF??... NO!
![Page 9: Factoring Trinomials. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)](https://reader036.vdocuments.us/reader036/viewer/2022081422/551b85ba550346a10a8b53d7/html5/thumbnails/9.jpg)
Practice
Factor the following:
1. x2 + 9x + 8
2. x2 – 12x + 10
3. x2 – 2x – 3
4. x2 + 8x + 15
![Page 10: Factoring Trinomials. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)](https://reader036.vdocuments.us/reader036/viewer/2022081422/551b85ba550346a10a8b53d7/html5/thumbnails/10.jpg)
Factoring with GCF
• *****Always look for a GCF first*****• Ex. 4x2 – 12x – 16• What is the GCF?• 4(x2 – 3x – 4)• Can we factor x2 – 3x – 4 more?• Are there two numbers that multiply to equal -4
and add to be -3?• x2 – 3x – 4 factors to (x – 4)(x + 1)• Final answer: 4(x – 4)(x + 1)
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Factoring with GCF
• Example 2: 6x2 + 30x + 36• GCF?• 6• 6(x2 + 5x + 6)• Can be x2 + 5x + 6 factored?
x2 + 5x + 6 can be factored to (x + 3)(x + 2)• Answer: 6(x + 3)(x + 2)
![Page 12: Factoring Trinomials. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)](https://reader036.vdocuments.us/reader036/viewer/2022081422/551b85ba550346a10a8b53d7/html5/thumbnails/12.jpg)
Practice!!Practice!!2
3 2
3 2
2
2
3 2
1. 2 16 24
2. 3 9 30
3. 5 14
4. 3 27 60
5. 4 4 48
6. 2 4 48
x x
x x x
x x x
x x
x x
x x x
Factor eachPolynomial !!!
1.1.2(x + 2) (x + 2(x + 2) (x + 6)6)
2.2.3x(x + 5) (x – 3x(x + 5) (x – 2)2)
3.3.x(x + 7) (x – 2)x(x + 7) (x – 2)4.4.3(x + 5) (x + 3(x + 5) (x +
4)4)5.5.4(x – 4) (x + 4(x – 4) (x +
3)3)6.6.2x(x - 6)(x + 2x(x - 6)(x +
4)4)
Don’t forget the GCF!
![Page 13: Factoring Trinomials. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5) 3. (x + 2)(x + 9) 4. (x – 4)(x – 6)](https://reader036.vdocuments.us/reader036/viewer/2022081422/551b85ba550346a10a8b53d7/html5/thumbnails/13.jpg)
Class work-begin Factoring WS
Homework-Finish Factoring WS