Question

the expression $x^2y - 2xy - 24y$ can be factored by first factoring out a common factor of $y$.

after the common factor is removed, the remaining factor is a

Explanation:

Step1: Factor out common term $y$

$x^2y - 2xy - 24y = y(x^2 - 2x - 24)$

Step2: Factor the quadratic expression

Find two numbers that multiply to $-24$ and add to $-2$: $-6$ and $4$.
$x^2 - 2x - 24 = (x - 6)(x + 4)$

Answer:

The remaining factor after removing $y$ is $x^2 - 2x - 24$, which can be further factored to $(x-6)(x+4)$. The unfactored quadratic remaining after extracting $y$ is $\boldsymbol{x^2 - 2x - 24}$.