Question

type the correct answer in the box.
write this expression in its most simplified, factored form.
12x²y - 32xy + 8y
do not include multiplication symbols (· or ×) between factors.

Explanation:

Step1: Factor out GCF

Identify and factor the greatest common factor of all terms.
$12x^2y - 32xy + 8y = 4y(3x^2 - 8x + 2)$

Step2: Check quadratic factor

Verify if the quadratic trinomial can be factored further. The discriminant of $3x^2 - 8x + 2$ is $\Delta = (-8)^2 - 4(3)(2) = 64 - 24 = 40$, which is not a perfect square, so it cannot be factored into integer binomials.

Answer:

$4y(3x^2 - 8x + 2)$