Question

What is the completely factored form of the expression 2x¹⁶ - 32x⁴?

a) 2x(x¹⁵ - 18x³)
b) 2x⁴(x⁶ + 4)(x³ - 2)(x³ + 2)
c) 2x⁴(x² + 4)(x + 4)(x - 4)
d) (2x⁴ - 32x²)(x⁴ + 4)

Answer 1

The completely factored form of the expression 2x¹⁶ - 32x⁴ is 2x⁴(x⁶ + 4)(x³ - 2)(x³ + 2).

Step-by-step explanation:

The completely factored form of the expression 2x¹⁶ - 32x⁴ is option b) 2x⁴(x⁶ + 4)(x³ - 2)(x³ + 2).

To completely factor the expression, we can start by factoring out the greatest common factor of 2x⁴ from both terms:

2x⁴(x¹² - 16).

Next, we recognize that x¹² - 16 is a difference of squares and can be factored as (x⁶ + 4)(x³ - 2)(x³ + 2).

So, the completely factored form of the expression is 2x⁴(x⁶ + 4)(x³ - 2)(x³ + 2).