Question

what is the completely factored form of the expression $16x^2 + 8x + 32$?
$\bigcirc\\ 4(4x^2 + 2x + 8)$
$\bigcirc\\ 4(12x^2 + 4x + 28)$
$\bigcirc\\ 8(2x^2 + x + 4)$
$\bigcirc\\ 8x(8x^2 + x + 24)$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 16, 8, 32. The greatest common factor (GCF) is 8.

Step2: Factor out the GCF

Divide each term by 8:
$16x^2 \div 8 = 2x^2$, $8x \div 8 = x$, $32 \div 8 = 4$
So factored form: $8(2x^2 + x + 4)$

Step3: Verify options

Check if the factored expression matches any option, and confirm the quadratic inside has no further rational factors (discriminant: $1^2 - 4(2)(4) = 1 - 32 = -31 < 0$, so no real/rational factors).

Answer:

C. $8(2x^2 + x + 4)$