Question

Factor completely.
2f2+13f+11

Answer 1

To factor the quadratic expression \(2f^2 + 13f + 11\), we look for two numbers that multiply to \(2 \times 11 = 22\) and add up to \(13\).

The two numbers that meet these criteria are \(11\) and \(2\), since \(11 \times 2 = 22\) and \(11 + 2 = 13\).

Now we can rewrite the middle term \(13f\) using \(11f\) and \(2f\):

\[
2f^2 + 11f + 2f + 11
\]

Next, we group the terms:

\[
(2f^2 + 11f) + (2f + 11)
\]

Now, factor by grouping:

1. From the first group \(2f^2 + 11f\), we can factor out \(f\):
\[
f(2f + 11)
\]

2. From the second group \(2f + 11\), we can factor out \(1\):
\[
1(2f + 11)
\]

Now we have:

\[
f(2f + 11) + 1(2f + 11)
\]

Factor out the common term \((2f + 11)\):

\[
(2f + 11)(f + 1)
\]

Thus, the completely factored form of the quadratic expression \(2f^2 + 13f + 11\) is:

\[
(2f + 11)(f + 1)
\]