Question

Factor the trinomial:
5, x, squared, plus, 33, x, plus, 18
5x
2
+33x+18

Answer 1

To factor the trinomial \( 5x^2 + 33x + 18 \), we look for two numbers that multiply to \( 5 \times 18 = 90 \) and add to \( 33 \).

The two numbers that work are \( 30 \) and \( 3 \) since:
- \( 30 + 3 = 33 \)
- \( 30 \times 3 = 90 \)

Next, we rewrite the middle term using these two numbers:

\[
5x^2 + 30x + 3x + 18
\]

Now, we can group the terms:

\[
(5x^2 + 30x) + (3x + 18)
\]

Factoring each group gives:

\[
5x(x + 6) + 3(x + 6)
\]

Now we can factor out the common term \( (x + 6) \):

\[
(5x + 3)(x + 6)
\]

Thus, the factored form of the trinomial \( 5x^2 + 33x + 18 \) is:

\[
\boxed{(5x + 3)(x + 6)}
\]