Question

Factor completely.
2w2+9w+10

Answer 1

To factor the quadratic expression \(2w^2 + 9w + 10\), we look for two numbers that multiply to the product of the coefficient of \(w^2\) (which is 2) and the constant term (which is 10). Thus, we need two numbers that multiply to \(2 \times 10 = 20\) and add to \(9\).

The numbers that fit this are \(4\) and \(5\) because:

- \(4 + 5 = 9\)
- \(4 \times 5 = 20\)

Next, we rewrite the middle term \(9w\) using \(4w\) and \(5w\):

\[
2w^2 + 4w + 5w + 10
\]

Now, we can group the terms:

\[
(2w^2 + 4w) + (5w + 10)
\]

Factoring out the common terms from each group:

\[
2w(w + 2) + 5(w + 2)
\]

Now, we notice that both groups contain the factor \((w + 2)\):

\[
(2w + 5)(w + 2)
\]

Thus, the completely factored form of \(2w^2 + 9w + 10\) is:

\[
\boxed{(2w + 5)(w + 2)}
\]