Question

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)

Answer 1

• 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)

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