Question

what is the completely factored form of $2x^2 - 32$?$(2x^2 + 16)(x - 16)$$2(x + 4)(x - 4)$$2(x + 8)(x - 4)$$2(x - 8)(x - 4)$done

Explanation:

Step1: Factor out the GCF

Factor out 2 from the expression:
$2x^2 - 32 = 2(x^2 - 16)$

Step2: Apply difference of squares

Use $a^2 - b^2=(a+b)(a-b)$ for $x^2 - 16$:
$x^2 - 16 = (x+4)(x-4)$

Step3: Combine the factors

Substitute back into the expression:
$2(x^2 - 16) = 2(x+4)(x-4)$

Answer:

2(x + 4)(x - 4)