1. 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)

2. Add or subtract.
G. 2x8 + 7y8 – x8 – y8
2x8 + 7y8 – x8 – y8
x8 + 6y8
H. 9b3c2 + 5b3c2 – 13b3c2
9b3c2 + 5b3c2 – 13b3c2
b3c2

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

4. Recall that a polynomial is in its fully factored form when it is written as a product that cannot be factored further.

5. 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

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

7. Tell whether the polynomial is completely factored. If not, factor it.
A. 5x2(x – 1)
completely factored
B. (4x + 4)(x + 1)
4x + 4 can be further factored.
4(x + 1)(x + 1)
Factor out 4, the GCF of 4x and 4.
4(x + 1)2 is completely factored.

8. To factor a polynomial completely, you may need to use more than one factoring method. Use the steps below to factor a polynomial completely.

9. Factor 10x2 + 48x + 32 completely.
Factor out the GCF.
2(5x + 4)(x + 4)
Factor remaining trinomial.

10. Factor 8x6y2 – 18x2y2 completely.
Factor out the GCF. 4x4 – 9 is a perfect-square binomial of the form a2 – b2.
2x2y2(4x4 – 9)
2x2y2(2x2 – 3)(2x2 + 3)

11. Factor each polynomial completely.
4x3 + 16x2 + 16x
Factor out the GCF. x2 + 4x + 4 is a perfect-square trinomial of the form a2 + 2ab + b2.
4x(x + 2)2

12. 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

13. Factor each polynomial completely.
9x2 + 3x – 2
The GCF is 1 and there is no pattern.
9x2 + 3x – 2

14. 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.

15. 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.

16. 3q4(3q2 + 10q + 8) Factor each polynomial completely.
Factor out the GCF. There is no pattern.
3q4(3q2 + 10q + 8)
9q6 + 30q5 + 24q4

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