Question

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

Answer 1

Answer:

• 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