8-6 Choosing a Factoring Method
Warm Up
Factor each trinomial.
1. x2 + 13x + 40 (x + 5)(x + 8)
2. 5x2 – 18x – 8 (5x + 2)(x – 4)
3. Factor the perfect-square trinomial
16x2 + 40x + 25 (4x + 5)(4x + 5)
4. Factor 9x2 – 25y2 using the difference of
two squares. (3x + 5y)(3x – 5y)
Holt Algebra 1
8-6 Choosing a Factoring Method
Add or subtract.
G. 2x8 + 7y8 – x8 – y8
2x8 + 7y8 – x8 – y8
x8 + 6y8
H. 9b3c2 + 5b3c2 – 13b3c2
9b3c2 + 5b3c2 – 13b3c2
b3c2
Holt Algebra 1
8-6 Choosing a Factoring Method
Learning Targets
Students will be able to: Choose an
appropriate method for factoring a
polynomial and combine methods for
factoring a polynomial.
Holt Algebra 1
8-6 Choosing a Factoring Method
Recall that a polynomial is in its fully factored
form when it is written as a product that cannot
be factored further.
Holt Algebra 1
8-6 Choosing a Factoring Method
Tell whether each polynomial is completely
factored. If not factor it.
A. 3x2(6x – 4)
6x – 4 can be further factored.
6x2(3x – 2)
Factor out 2, the GCF of 6x and – 4.
completely factored
B. (x2 + 1)(x – 5)
completely factored
Holt Algebra 1
8-6 Choosing a Factoring Method
Caution
x2 + 4 is a sum of squares, and cannot be
factored.
Holt Algebra 1
8-6 Choosing a Factoring Method
Tell whether the polynomial is completely
factored. If not, factor it.
A. 5x2(x – 1)
completely factored
B. (4x + 4)(x + 1)
4(x + 1)(x + 1)
4x + 4 can be further factored.
Factor out 4, the GCF of 4x and 4.
4(x + 1)2 is completely factored.
Holt Algebra 1
8-6 Choosing a Factoring Method
To factor a polynomial completely, you may need
to use more than one factoring method. Use the
steps below to factor a polynomial completely.
Holt Algebra 1
8-6 Choosing a Factoring Method
Factor 10x2 + 48x + 32 completely.
10x2 + 48x + 32
2(5x2 + 24x + 16)
Factor out the GCF.
2(5x + 4)(x + 4)
Factor remaining trinomial.
4 20x 16
x 5x 2 4x
5x
Holt Algebra 1
4
80x 2
20x 4x
24x
8-6 Choosing a Factoring Method
Factor 8x6y2 – 18x2y2 completely.
8x6y2 – 18x2y2
2x2y2(4x4 – 9)
2x2y2(2x2 – 3)(2x2 + 3)
Holt Algebra 1
Factor out the GCF. 4x4 – 9 is a
perfect-square binomial of the
form a2 – b2.
8-6 Choosing a Factoring Method
Factor each polynomial completely.
4x3 + 16x2 + 16x
4 x  x2  4 x  4
4x  x  2 x  2
4x(x + 2)2
Holt Algebra 1
Factor out the GCF. x2 + 4x + 4 is a
perfect-square trinomial of the
form a2 + 2ab + b2.
8-6 Choosing a Factoring Method
If none of the factoring methods work, the polynomial
is said to be unfactorable.
Helpful Hint
For a polynomial of the form ax2 + bx + c, if
there are no numbers whose sum is b and whose
product is ac, then the polynomial is
unfactorable.
Holt Algebra 1
8-6 Choosing a Factoring Method
Factor each polynomial completely.
9x2 + 3x – 2
2 6x 2
3x 9x 2 3x
3x 1
9x2 + 3x – 2
Holt Algebra 1
The GCF is 1 and there is no
pattern.
18x 2
6x 3x
3x
 3x 13x  2
8-6 Choosing a Factoring Method
Factor each polynomial completely.
12b3 + 48b2 + 48b The GCF is 12b; (b2 + 4b + 4)
is a perfect-square
2
12b b  4b  4
trinomial in the form of
2 + 2ab + b2.
a
12b b  2 b  2



 12b  b  2 
Holt Algebra 1

2

8-6 Choosing a Factoring Method
Factor each polynomial completely.
4y2 + 12y – 72
Factor out the GCF.
4(y2 + 3y – 18)
4(y – 3)(y + 6)
(x4 – x2)
x2(x2 – 1)
Factor out the GCF.
x2(x + 1)(x – 1)
x2 – 1 is a difference of two
squares.
Holt Algebra 1
8-6 Choosing a Factoring Method
Factor each polynomial completely.
9q6 + 30q5 + 24q4
3q4(3q2 + 10q + 8)
Factor out the GCF. There is no
pattern.
2
2 6q 8
q 3q 2 4q
24q
6q 4q
10q
3q 4
9q6
+
Holt Algebra 1
30q5
+
24q4
 3q 3q  4 q  2
4
8-6 Choosing a Factoring Method
HW pp. 569-571/19-35 odd,40-72 even
Holt Algebra 1