1. 8.6 Choosing a Factoring Method

2. California
Standards
11.0 Students apply basic factoring techniques to second- and simple third- degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.

3. Check
1. GCF 2. Difference of two squares (2 terms) 3. Factor by grouping (4 terms) 4. X method (x2 + 8x + 12) 5. Perfect squares 6. x and box method (4x2 + 16x + 15)

4. Tell whether each expression is completely factored. If not, factor it.
(x2 + 1)(x – 5)
1. GCF 2. Difference of two squares (2 terms) 3. Factor by grouping (4 terms) 4. X method (x2 + 8x + 12) 5. Perfect squares 6. x and box method (4x2 + 16x + 15)
Yes

5. B. 5x(x2 – 2x – 3) 5x(x2 – 2x – 3) 5x(x + 1)(x – 3) 5x(x + 1)(x – 3)
Tell whether each expression is completely factored. If not, factor it.
B. 5x(x2 – 2x – 3)
1. GCF 2. Difference of two squares (2 terms) 3. Factor by grouping (4 terms) 4. X method (x2 + 8x + 12) 5. Perfect squares 6. x and box method (4x2 + 16x + 15)
5x(x2 – 2x – 3)
5x(x + 1)(x – 3)
5x(x + 1)(x – 3)
Product -3 -3 1 -2
sum

6. C. 8x6y2 – 18x2y2 Not done 2x2y2(2x2 – 3)(2x2 + 3) 8x6y2 – 18x2y2 2
Tell whether each expression is completely factored. If not, factor it.
C. 8x6y2 – 18x2y2
1. GCF 2. Difference of two squares (2 terms) 3. Factor by grouping (4 terms) 4. X method (x2 + 8x + 12) 5. Perfect squares 6. x and box method (4x2 + 16x + 15)
8x6y2 – 18x2y2 2
4x6y2 – 9x2y2 x2
4x4y2 – 9y2 y2
4x4 – 9
Not done
2x2y2(4x4 – 9)
2x2y2(2x2 – 3)(2x2 + 3)

7. D. 2x2y – 2y3 Not done 2x2y – 2y3 2 x2y – y3 y x2 – y2 2y(x2 – y2)
Tell whether each expression is completely factored. If not, factor it.
D. 2x2y – 2y3
1. GCF 2. Difference of two squares (2 terms) 3. Factor by grouping (4 terms) 4. X method (x2 + 8x + 12) 5. Perfect squares 6. x and box method (4x2 + 16x + 15)
2x2y – 2y3 2
x2y – y3 y
x2 – y2
Not done
2y(x2 – y2)
2y(x – y)(x + y)

8. E. 12b3 + 48b2 + 48b Product sum 12b3 + 48b2 + 48b 12 b3 + 4b2 + 4b b
Tell whether each expression is completely factored. If not, factor it.
E. 12b3 + 48b2 + 48b
12b3 + 48b2 + 48b
1. GCF 2. Difference of two squares (2 terms) 3. Factor by grouping (4 terms) 4. X method (x2 + 8x + 12) 5. Perfect squares 6. x and box method (4x2 + 16x + 15) 12
b3 + 4b2 + 4b b
b2 + 4b + 4
12b(b2 + 4b + 4)
Product
12b(b + 2)(b+ 2) 4
12b(b + 2)2 2 2 4
sum

9. Factor completely
2p3(p + 6)(p – 1)
2p5 + 10p4 – 12p3
4x3 + 16x2 + 16x
4y2 + 12y – 72
2x2 + 20x + 32
9q3 + 30q2 + 24q
4x(x + 2)2
4(y – 3)(y + 6)
2(x + 8)(x + 2)
3q(3q + 4)(q + 2)

11. Lesson Quiz
Tell whether the polynomial is completely factored. If not, factor it.
1. (x + 3)(5x + 10) x2(x2 + 9)
no; 5(x+ 3)(x + 2)
completely factored
Factor each polynomial completely. Check your answer.
3. x3 + 4x2 + 3x x2 + 16x – 48
4(x + 6)(x – 2)
(x + 4)(x2 + 3)
5. 18x2 – 3x – 3
6. 18x2 – 50y2
3(3x + 1)(2x – 1)
2(3x + 5y)(3x – 5y)
7. 5x – 20x3 + 7 – 28x2
(1 + 2x)(1 – 2x)(5x + 7)