Question

Crystal has the trinomial 2n2 + 5n + 2 on her math homework. Which of the following expressions is the factored form of the trinomial?

Group of answer choices

(2n − 1)(n + 2)

(n − 1)(n + 2)

(2n + 1)(n + 2)

(2n − 1)(n − 2)

Answer 1

To factor the trinomial \( 2n^2 + 5n + 2 \), we need to break it down into two binomials.

We can look for two numbers that multiply to \( 2 \times 2 = 4 \) (the coefficient of \( n^2 \) multiplied by the constant term) and add up to \( 5 \) (the coefficient of \( n \)).

The numbers \( 4 \) and \( 1 \) work because:
- \( 4 \times 1 = 4 \)
- \( 4 + 1 = 5 \)

Now, we can rewrite the middle term \( 5n \) using \( 4n \) and \( 1n \):
\[
2n^2 + 4n + 1n + 2
\]

Next, we group the terms:
\[
(2n^2 + 4n) + (1n + 2)
\]

Now, we factor each group:
\[
2n(n + 2) + 1(n + 2)
\]

We see that \( (n + 2) \) is a common factor:
\[
(2n + 1)(n + 2)
\]

So, the factored form of the trinomial \( 2n^2 + 5n + 2 \) is:
\[
(2n + 1)(n + 2)
\]

Among the provided choices, the correct one is:
**(2n + 1)(n + 2)**.