Question

Factor completely.
k2+13k+22

Answer 1

To factor the quadratic expression \( k^2 + 13k + 22 \), we will look for two numbers that multiply to \( 22 \) (the constant term) and add up to \( 13 \) (the coefficient of the linear term).

The factors of \( 22 \) are:
- \( 1 \) and \( 22 \)
- \( 2 \) and \( 11 \)

Now, let's check which pair adds up to \( 13 \):
- \( 1 + 22 = 23 \) (not a match)
- \( 2 + 11 = 13 \) (this is a match)

Therefore, we can factor the expression as follows:

\[
k^2 + 13k + 22 = (k + 2)(k + 11)
\]

So, the completely factored form of \( k^2 + 13k + 22 \) is:

\[
\boxed{(k + 2)(k + 11)}
\]