Question

type the correct answer in the box.

write this expression in its most simplified, factored form.

(12x^2y - 32xy + 8y)

do not include multiplication symbols (\\(\cdot\\) or \\(\times\\)) between factors.

Explanation:

Factor out the greatest common factor (GCF)

$$ \text{GCF}(12x^2y, -32xy, 8y) = 4y $$

$$ 12x^2y - 32xy + 8y = 4y(3x^2 - 8x + 2) $$

Verify if the remaining trinomial can be factored further

$$ 3x^2 - 8x + 2 $$

$$ D = (-8)^2 - 4(3)(2) = 64 - 24 = 40 $$

Since \(40\) is not a perfect square, the quadratic trinomial \(3x^2 - 8x + 2\) cannot be factored further over the integers.

Answer:

Write this expression in its most simplified, factored form.

\(12x^2y - 32xy + 8y =\) <blank>\(4y(3x^2 - 8x + 2)\)</blank>