Match each polynomial in standard form to its equivalent factored form.

8x^3+1

2x^4+16x

x^3+8

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

The polynomial cannot be factored over the integers using the sum of cubes method.

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

(x+8) (x^2-16x+64)

(2x+16) (4x^2-32x+64)

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

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

8x^3+1 ⇒ (2x+1) (4x^2-2x+1) 2x^4+16x ⇒ 2x (x+2) (x^2-2x+4) x^3+8 ⇒ (x+2) (x^2-2x+4)

Step-by-step explanation:

The factoring of the sum of cubes is ...

a³ + b³ = (a + b) (a² - ab + b²)

1. a=2x, b=1

= (2x) ³ + 1³

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2. There is an overall factor of 2x. Once that is factored out, a=x, b=2.

= (2x) (x³ + 2³)

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3. a=x, b=2

= x³ + 2³