Question

Factor the polynomial: 2x3 + 16 Question 15 options:

A) 2(x + 2)(x + 4)
B) 2(x + 2)(x2 – 2x + 4)
C) 2(x + 2)(x2 + 2x + 4)
D) 2(x + 2)(x – 2)2

Answer 1

B

Explanation:

Given

2x³ + 16 ← factor out 2 from each term

= 2(x³ + 8) ← x³ + 8 is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b²) , then

x³ + 8

= x³ + 2³

= (x + 2)(x² - 2x + 2²)

= (x + 2)(x² - 2x + 4)

Then

2x³ + 16 = 2(x + 2)(x² - 2x + 4) ← in factored form → B