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Algebra 1
Objective:
Lesson Notes 9.8A
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Factor polynomials by grouping.
We know that when factoring we must: ALWAYS factor out the GCF first !
Sometimes the GCF is a binomial.
Example 1 (p 606): Factor out a common binomial.
Factor the expression.
a.
4 x  x  3  5  x  3  
b.
2 y 2  y  5  3 5  y  
←
If necessary, factor out a −1 to
get a common binomial factor.
Sometimes in a polynomial with four terms, we have to find the common binomial using a
process called factoring by grouping.
factoring by grouping:
Group the terms.
Factor the GCF out of the groups.
Factor out the common binomial.
Example 2 (p 606): Factor by grouping.
a.
x3  2 x2  8x  16
b.
n2  4n  nt  4t
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If necessary, rearrange the terms in the polynomial so that you can group terms with a common
factor.
Example 3 (p 607): Factor by grouping.
Factor x3  10  5x  2 x2
 HW:
A11a p610 #6-20
A11b Lesson 9.8 Practice B #1-12
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Algebra 1
Lesson Notes 9.8B
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Objective: Factor polynomials completely.
A factorable polynomial is factored completely if it is written as the product of unfactorable
polynomials with integer coefficients.
Guidelines for Factoring Polynomials Completely:
1. Factor out the greatest common monomial factor.
2. Look for a difference of squares or a perfect square trinomial.
3. Factor a trinomial of the form ax2  bx  c into the product of two binomials.
4. Factor a polynomial with four terms by grouping.
Note: Some polynomials are not factorable.
Example 4 (p 608): Factor completely.
Factor the polynomial completely.
a.
x2  4 x  3
b.
3x3  21x2  54 x
c.
8d 3  24d
d.
2 x3  3x2  8x  12
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Example 5 (p 608): Solve a polynomial equation.
Solve 2 x3  18x2   36 x
Example 6 (p 608): Solve a multi-step equation.
A kitchen drawer has a volume of 768 cubic inches. The dimensions of the drawer are
shown.
16 – w
w
w+4
a. Find the length, width, and depth of the drawer.
b. If you know that a 6 inch deep pot does not fit in the drawer, what
does that tell you about your answer?
 HW:
A12a pp 610-612 #28-38 even, 44-52 even, 69-70
A12b Lesson 9.8 Practice B #14-30 even, 31-33
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