Question

Factor the trinomial:
5, x, squared, plus, 13, x, plus, 6
5x
2
+13x+6

Answer 1

To factor the trinomial \( 5x^2 + 13x + 6 \), we will look for two numbers that multiply to \( 5 \times 6 = 30 \) (the product of the coefficient of \( x^2 \) and the constant term) and add up to \( 13 \) (the coefficient of \( x \)).

The numbers that work are \( 3 \) and \( 10 \), since:

- \( 3 \times 10 = 30 \)
- \( 3 + 10 = 13 \)

Now, we can rewrite the middle term (the \( 13x \)) using these two numbers:

\[
5x^2 + 3x + 10x + 6
\]

Next, we can group the terms:

\[
(5x^2 + 3x) + (10x + 6)
\]

Now, we factor by grouping:

1. Factor out \( x \) from the first group and \( 2 \) from the second group:

\[
x(5x + 3) + 2(5x + 3)
\]

2. Now, we can factor out the common binomial \( (5x + 3) \):

\[
(5x + 3)(x + 2)
\]

Thus, the factorization of the trinomial \( 5x^2 + 13x + 6 \) is:

\[
\boxed{(5x + 3)(x + 2)}
\]