Question

Factor completely.
2m2+11m+9

Answer 1

To factor the quadratic expression \(2m^2 + 11m + 9\), we can use the method of factoring by grouping.

First, we need to find two numbers that multiply to \(2 \times 9 = 18\) (the product of the leading coefficient and the constant) and add to \(11\) (the coefficient of the middle term).

The two numbers that meet these criteria are \(2\) and \(9\) since:
- \(2 \times 9 = 18\)
- \(2 + 9 = 11\)

Next, we can rewrite the middle term \(11m\) using \(2m\) and \(9m\):

\[
2m^2 + 2m + 9m + 9
\]

Now, we can group the terms:

\[
(2m^2 + 2m) + (9m + 9)
\]

Next, we factor out the common factors in each group:

\[
2m(m + 1) + 9(m + 1)
\]

Now, we can factor out the common binomial factor \((m + 1)\):

\[
(m + 1)(2m + 9)
\]

Thus, the completely factored form of \(2m^2 + 11m + 9\) is:

\[
\boxed{(m + 1)(2m + 9)}
\]