Question
Factor completely.
2h2+13h+6
2h2+13h+6
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Answered by
GPT-4o mini
To factor the quadratic expression \( 2h^2 + 13h + 6 \), we'll look for two numbers that multiply to \( 2 \times 6 = 12 \) and add up to \( 13 \).
The two numbers that fit this requirement are \( 12 \) and \( 1 \).
Next, we can rewrite the middle term (13h) using these two numbers:
\[
2h^2 + 12h + 1h + 6
\]
Now, we can group the terms:
\[
(2h^2 + 12h) + (1h + 6)
\]
Factoring each group, we have:
\[
2h(h + 6) + 1(h + 6)
\]
Now we can factor out the common factor \((h + 6)\):
\[
(h + 6)(2h + 1)
\]
Thus, the complete factorization of \( 2h^2 + 13h + 6 \) is:
\[
\boxed{(h + 6)(2h + 1)}
\]
The two numbers that fit this requirement are \( 12 \) and \( 1 \).
Next, we can rewrite the middle term (13h) using these two numbers:
\[
2h^2 + 12h + 1h + 6
\]
Now, we can group the terms:
\[
(2h^2 + 12h) + (1h + 6)
\]
Factoring each group, we have:
\[
2h(h + 6) + 1(h + 6)
\]
Now we can factor out the common factor \((h + 6)\):
\[
(h + 6)(2h + 1)
\]
Thus, the complete factorization of \( 2h^2 + 13h + 6 \) is:
\[
\boxed{(h + 6)(2h + 1)}
\]
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