Question

completely factor the given polynomial. if the polynomial cannot be factored, write nf for your answer.

\xy + 9y - 13x - 117\\

Explanation:

Group the polynomial terms

Using the Factoring by Grouping knowledge point, we group the four-term polynomial into two pairs:

$$ (xy + 9y) + (-13x - 117) $$

Factor the first group

We find the greatest common factor of the first group \(xy + 9y\), which is \(y\):

$$ y(x + 9) $$

Factor the second group

We find the greatest common factor of the second group \(-13x - 117\), which is \(-13\):

$$ -13(x + 9) $$

Extract the common binomial factor

Both terms now share a common binomial factor of \((x + 9)\). We factor this out:

$$ (x + 9)(y - 13) $$

Answer:

\((x + 9)(y - 13)\)