Question

Look for a GCF first, then trinomial or difference of 2 squares

1. 2x3 - 32x
2. 4x2 + 24x + 20

Answer 1

1. 2x(x - 4)(x + 4)

2. 4(x + 1)(x + 5)

Explanation:

1. 2x³ - 32x

2x(x² - 16)

2x(x² - 4²)

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

2. 4x² + 24x + 20

4(x² + 6x + 5)

4(x² + 5x + x + 5)

4[x(x + 5) + 1(x + 5)]

4(x + 1)(x + 5)

Answer 2

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

4(x+3)(x+2)

Explanation:

1. 2x^3 - 32x

Factor out 2x

2x(x^2 - 16)

2x( x^2 - 4^2)

This is the difference of squares ( a^2 - b^2) = (a-b) (a+b)

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

2. 4x^2 + 24x + 20

Factor out 4

4 (x^2 +6x +5)

What 2 numbers multiply to 5 and add to 6

3*2 =6

3+2 =5

4(x+3)(x+2)