Question

Match each polynomial with its correct factoring method. You will use each factoring method only once!

Answer 1

Answer:

1. 16x2−40x+25

Perfect Square Trinomial

2. x2−2x−8

Trinomial when A>1

3. 3x2+6xy+9xy2

Greatest Common Factor (GCF)

4. 64x2−100

Difference of Squares

5. 27x3+8y6

Sum of Cubes

6. 64x9−y3

Difference of Cubes

7. 6x2+19x+15

Trinomial when A=1

8. 6x3+3x2+8x+4

Grouping

Step-by-step explanation:

A trinomial is a polynomial which has three terms.

1. 16x2−40x+25

(4x)2 - 2(4x)(5) + (5)2

= (4x-5)2

Perfect Square Trinomial

2. x2−2x−8

= x2 - 4x+2x-8

= x(x-4) +2 (x-4)

= (x+2)(x-4)

Trinomial when A>1 ( when we will put x= 1 we will get a negative value)

3. 3x2+6xy+9xy2

=3x(x+2y+3y2)

(3x is common)

Greatest Common Factor (GCF)

4. 64x2−100

= (8x)2- (10)2

= (8x-10)(8x+10)

Difference of Squares

5. 27x3+8y6

=(3x)3+(2y2)3

= (3x+2y)(6x2-6xy+4y2)

Sum of Cubes

6. 64x9−y3

= (4x3)3- (y)3

Difference of Cubes

7. 6x2+19x+15

= 6x2 + 9x + 10x + 15

= 3x( 2x+3) + 5(2x+3)

= (2x+3)(3x+5)

Trinomial when A=1

8. 6x3+3x2+8x+4

Grouping

Grouping usually has four or more terms

6x3+3x2+8x+4

=3x2(2x+1) + 4(2x+1)

=(3x2+4) (2x+1)