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)

Question

asked May 18, 2024 167k views

1 Answer

Soroushjp · Answer 1 · 2024-05-24T05:42:44+0000

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

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).