8-2 Factoring by GCF
Warm Up
Simplify.
1. 2(w + 1) 2w + 2
2. 3x(x2 – 4) 3x3 – 12x
Find the GCF of each pair of monomials.
3. 4h2 and 6h 2h
4. 13p and 26p5 13p
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8-2 Factoring by GCF
Find the value of each power of 10.
a. 10–2
0.01
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b. 105
100,000
c. 1010
10,000,000,000
8-2 Factoring by GCF
Objective
Factor polynomials by using the
greatest common factor.
Holt Algebra 1
8-2 Factoring by GCF
Recall that the Distributive Property states that
ab + ac =a(b + c). The Distributive Property
allows you to “factor” out the GCF of the terms in
a polynomial to write a factored form of the
polynomial.
A polynomial is in its factored form when it is
written as a product of monomials and polynomials
that cannot be factored further. The polynomial
2(3x – 4x) is not fully factored because the terms
in the parentheses have a common factor of x.
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8-2 Factoring by GCF
Factor each polynomial. Check your answer.
 2  x  2
2x2 – 4
2
 4x  2x  x  4
8x3 – 4x2 – 16x
2
–14x – 12x2
 2 x  7  6 x 
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8-2 Factoring by GCF
Factor each polynomial.
3x3 + 2x2 – 10
The polynomial cannot be factored further.
–18y3 – 7y2
  y 18 y  7 
2
8x4 + 4x3 – 2x2
 2 x  4 x  2 x  1
2
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2
8-2 Factoring by GCF
The area of a court for the game squash is
9x2 + 6x m2. Factor this polynomial to find
possible expressions for the dimensions of
the squash court.
 3x  3 x  2 
Possible expressions for the dimensions of the
squash court are 3x m and (3x + 2) m.
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8-2 Factoring by GCF
Sometimes the GCF of terms is a binomial. This
GCF is called a common binomial factor. You
factor out a common binomial factor the same
way you factor out a monomial factor.
Holt Algebra 1
8-2 Factoring by GCF
Factor each expression.
A. 5(x + 2) + 3x(x + 2)
The terms have a common
binomial factor of (x + 2).
Factor out (x + 2).
 x  25  3x 
B. –2b(b2 + 1)+ (b2 + 1)
b
2
 1  2b  1   b  1 1  2b 
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2
8-2 Factoring by GCF
Factor each expression.
C. 4z(z2 – 7) + 9(2z3 + 1)
There are no common
factors.
The expression cannot be factored.
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8-2 Factoring by GCF
Factor each expression.
a. 4s(s + 6) – 5(s + 6)
 s  6 4s  5
b. 7x(2x + 3) + (2x + 3)
 2x  3 7 x  1
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8-2 Factoring by GCF
You may be able to factor a polynomial by
grouping. When a polynomial has four terms,
you can make two groups and factor out the
GCF from each group.
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8-2 Factoring by GCF
Factor each polynomial by grouping.
Check your answer.
Group terms that have a common
4
3
6h – 4h + 12h – 8
number or variable as a factor.
(6h4 – 4h3) + (12h – 8)
2h3(3h – 2) + 4(3h – 2)
(3h – 2)(2h3 + 4)
Check (3h – 2)(2h3 + 4)
6h4 – 4h3 + 12h – 8
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8-2 Factoring by GCF
Factor each polynomial by grouping.
Check your answer.
5y4 – 15y3 + y2 – 3y
(5y4 – 15y3) + (y2 – 3y)
5y3(y – 3) + y(y – 3)
(y – 3)(5y3 + y)
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8-2 Factoring by GCF
Factor each polynomial by grouping.
Check your answer.
4r3 + 24r + r2 + 6
(4r3 + 24r) + (r2 + 6)
4r(r2 + 6) + 1(r2 + 6)
(r2 + 6)(4r + 1)
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8-2 Factoring by GCF
Helpful Hint
If two quantities are opposites, their sum is 0.
(5 – x) + (x – 5)
5–x+x–5
–x+x+5–5
0+0
0
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8-2 Factoring by GCF
Recognizing opposite binomials can help you factor
polynomials. The binomials (5 – x) and (x – 5) are
opposites. Notice (5 – x) can be written as –1(x – 5).
–1(x – 5) = (–1)(x) + (–1)(–5)
= –x + 5
Simplify.
=5–x
Commutative Property
of Addition.
So, (5 – x) = –1(x – 5)
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Distributive Property.
8-2 Factoring by GCF
Factor 2x3 – 12x2 + 18 – 3x
2x3 – 12x2 + 18 – 3x
(2x3 – 12x2) + (18 – 3x)
2x2(x – 6) + 3(6 – x)
2x2(x – 6) – 3(x – 6)
(x – 6)(2x2 – 3)
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8-2 Factoring by GCF
Factor each polynomial. Check your answer.
15x2 – 10x3 + 8x – 12
(15x2 – 10x3) + (8x – 12)
5x2(3 – 2x) + 4(2x – 3)
5x2(3 – 2x) – 4(3 – 2x)
(3 – 2x)(5x2 – 4)
HW pp. 535-537/27-39,41-53 Odd, 55-69, 71-86
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