Question

first factor out the greatest common factor from each term. then factor the remaining polynomial.
$2x^2 + 16x - 40$

select the correct choice below and fill in any answer box within your choice.
\\(\bigcirc\\) a. $2x^2 + 16x - 40 = \square$
\\(\bigcirc\\) b. $2x^2 + 16x - 40$ is prime.

Explanation:

Step1: Factor out GCF

Identify the greatest common factor (GCF) of $2x^2$, $16x$, and $-40$, which is 2.
$2x^2 + 16x - 40 = 2(x^2 + 8x - 20)$

Step2: Factor quadratic polynomial

Find two numbers that multiply to $-20$ and add to $8$ (these numbers are 10 and $-2$).
$x^2 + 8x - 20 = (x + 10)(x - 2)$

Step3: Combine factors

Substitute the factored quadratic back into the expression.
$2(x^2 + 8x - 20) = 2(x + 10)(x - 2)$

Answer:

A. $2x^2 + 16x - 40 = 2(x + 10)(x - 2)$