Given the expression [tex]\( x^2 y - 2 x y - 24 y \)[/tex], let's factor it step-by-step.
### Step-by-Step Solution:
1. Identify the Common Factor:
The expression [tex]\( x^2 y - 2 x y - 24 y \)[/tex] consists of three terms. Each term has a common factor of [tex]\( y \)[/tex]:
[tex]\[
x^2 y - 2 x y - 24 y = y(x^2 - 2x - 24)
\][/tex]
2. Factor Out the Common Factor:
When we factor out the common factor [tex]\( y \)[/tex] from each term, we are left with:
[tex]\[
y(x^2 - 2x - 24)
\][/tex]
3. Remaining Factor:
After removing the common factor [tex]\( y \)[/tex], the remaining factor is:
[tex]\[
x^2 - 2x - 24
\][/tex]
Hence, the expression [tex]\( x^2 y - 2 x y - 24 y \)[/tex] can be factored as [tex]\( y(x^2 - 2x - 24) \)[/tex]. After the common factor [tex]\( y \)[/tex] is removed, the remaining factor is:
[tex]\[
x^2 - 2x - 24
\][/tex]
