9.3 & 9.4 factoring trinomials by grouping p
DESCRIPTION
9.3 & 9.4 Factoring Trinomials by Grouping p. Review: (y + 2)(y + 4). First terms: Outer terms: Inner terms: Last terms: Combine like terms. In this lesson, we will begin with y 2 + 6y + 8 as our problem and finish with (y + 2)(y + 4) as our answer. Factor y 2 + 6y + 8. - PowerPoint PPT PresentationTRANSCRIPT
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9.3 & 9.4Factoring Trinomials
by Grouping
p.
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First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
y +2
y
+4
Review: (y + 2)(y + 4)
In this lesson, we will begin with y2 + 6y + 8 as our problem and finish with (y + 2)(y + 4) as our answer.
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Factor y2 + 6y + 8Do we have a GCF?
Is it a Diff. of Squares problem?
Now we will learn Trinomials! You will set up a table with the following information.
Product of the first and last coefficients
Middlecoefficient
The goal is to find two factors in the first column that add up to the middle term in the second column.
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Factor y2 + 6y + 8Create your table.
Multiply Add+8 +6
Product of the first and last coefficients
Middlecoefficient
Here’s your task…What numbers multiply to +8 and add to +6? If you cannot figure it out right away, write
the combinations.
M
A
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We have two groups!
Find the GCF of each group and factor it out.
You can check it by multiplying (FOIL).
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Factor x2 – 2x – 63 Do we have a GCF? NO! …
so, Create your table.Multiply AddProduct of the
first and last coefficients
Middlecoefficient
Signs need to be different
since number is negative.
M
A
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Replace the middle term with working numbers.
Group the terms.
Factor out the GCF
The parentheses are the same!
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Here are some hints to help you choose your factors in the table.
1) When the last term is positive, the factors will have the same sign as the middle term.
2) When the last term is negative, the factors will have different signs.
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Factor 5x2 - 17x + 14 Do we have a GCF? NO! …
so, create your table.Multiply Add
Replace the middle term.
Group the terms.
M
A
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Factor out the GCF
The parentheses are the same!
Hopefully, these will continue to get
easier the more you do them.
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Factor 2x2 - 14x + 12
Multiply Add
Find the GCF!
Signs need to be the same as
the middle sign since the
product is positive.
Replace the middle term.
Group the terms.
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Factor out the GCF
The parentheses are the same!
Remember: Always look for a GCF first!!
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Factor x2 + 3x + 21. (x + 2)(x + 1)
2. (x – 2)(x + 1)
3. (x + 2)(x – 1)
4. (x – 2)(x – 1)
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Factor 2x2 + 9x + 101. (2x + 10)(x + 1)
2. (2x + 5)(x + 2)
3. (2x + 2)(x + 5)
4. (2x + 1)(x + 10)
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Factor 6y2 – 13y – 51. (6y2 – 15y)(+2y – 5)
2. (2y – 1)(3y – 5)
3. (2y + 1)(3y – 5)
4. (2y – 5)(3y + 1)