Question

which expression is a factor of $5x^2 - 30x - 80$?\
\bigcirc $x + 4$\
\bigcirc $x + 8$\
\bigcirc $x - 4$\
\bigcirc $x - 8$

Explanation:

Step1: Factor out the GCF

$5x^2 - 30x - 80 = 5(x^2 - 6x - 16)$

Step2: Factor the quadratic trinomial

Find two numbers that multiply to $-16$ and add to $-6$: $-8$ and $2$.
$x^2 - 6x - 16 = (x - 8)(x + 2)$

Step3: Write full factored form

$5x^2 - 30x - 80 = 5(x - 8)(x + 2)$

Answer:

D. x-8