Holt Algebra 1

8-6 Choosing a Factoring Method

Warm UpFactor each trinomial.1. x2 + 13x + 402. 5x2 – 18x – 8 3. Factor the perfect-square trinomial

16x2 + 40x + 25 4. Factor 9x2 – 25y2 using the difference of two squares.

(x + 5)(x + 8)

(4x + 5)(4x + 5)

(5x + 2)(x – 4)

(3x + 5y)(3x – 5y)

Holt Algebra 1

8-6 Choosing a Factoring Method

G. 2x8 + 7y8 – x8 – y8

Add or subtract.

2x8 + 7y8 – x8 – y8 x8 + 6y8

H. 9b3c2 + 5b3c2 – 13b3c2 9b3c2 + 5b3c2 – 13b3c2 b3c2

Holt Algebra 1

8-6 Choosing a Factoring Method

Students will be able to: Choose an appropriate method for factoring a polynomial and combine methods for factoring a polynomial.

Learning Targets

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 MethodTell whether each polynomial is completely factored. If not factor it.

A. 3x2(6x – 4) 6x2(3x – 2)

B. (x2 + 1)(x – 5)

6x – 4 can be further factored.

Factor out 2, the GCF of 6x and – 4.completely factored

completely factored

Holt Algebra 1

8-6 Choosing a Factoring Method

x2 + 4 is a sum of squares, and cannot be factored.

Caution

Holt Algebra 1

8-6 Choosing a Factoring MethodTell whether the polynomial is completely factored. If not, factor it.

A. 5x2(x – 1)

B. (4x + 4)(x + 1)

Factor out 4, the GCF of 4x and 4.

4x + 4 can be further factored.

completely factored

4(x + 1)2 is completely factored.

4(x + 1)(x + 1)

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

2(5x2 + 24x + 16)

Factor 10x2 + 48x + 32 completely.

10x2 + 48x + 32

2(5x + 4)(x + 4)Factor out the GCF.

Factor remaining trinomial.

25x

16280x

24x20x 4x

20x

4x5x

x4

4

Holt Algebra 1

8-6 Choosing a Factoring MethodFactor 8x6y2 – 18x2y2 completely.

8x6y2 – 18x2y2

2x2y2(4x4 – 9)Factor out the GCF. 4x4 – 9 is a

perfect-square binomial of the form a2 – b2.

2x2y2(2x2 – 3)(2x2 + 3)

Holt Algebra 1

8-6 Choosing a Factoring MethodFactor each polynomial completely. 4x3 + 16x2 + 16x

4x(x + 2)2

Factor out the GCF. x2 + 4x + 4 is a perfect-square trinomial of the form a2 + 2ab + b2.

24 4 4x x x

4 2 2x x x

Holt Algebra 1

8-6 Choosing a Factoring Method

If none of the factoring methods work, the polynomial is said to be unfactorable.

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.

Helpful Hint

Holt Algebra 1

8-6 Choosing a Factoring MethodFactor each polynomial completely.

9x2 + 3x – 2 The GCF is 1 and there is no pattern.

29x

2218x

3x6x 3x

6x

3x3x

3x

2

1

9x2 + 3x – 2 3 1 3 2x x

Holt Algebra 1

8-6 Choosing a Factoring Method

212 4 4b b b

Factor each polynomial completely.12b3 + 48b2 + 48b The GCF is 12b; (b2 + 4b + 4)

is a perfect-square trinomial in the form of a2 + 2ab + b2. 12 2 2b b b

212 2b b

Holt Algebra 1

8-6 Choosing a Factoring Method

4(y2 + 3y – 18)

Factor each polynomial completely.4y2 + 12y – 72 Factor out the GCF.

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

3q4(3q2 + 10q + 8)

Factor each polynomial completely. Factor out the GCF. There is no

pattern.9q6 + 30q5 + 24q4

23q

8224q

10q6q 4q

6q

4q3q

q2

4

9q6 + 30q5 + 24q4 43 3 4 2q q q

Holt Algebra 1

8-6 Choosing a Factoring Method

HW pp. 569-571/19-35 odd,40-72 even