Question

Factor the quadratic expression 2x2+7x+3
(1 point)
Responses

(2x+3)(x+1)
(2x+3)(x+1)

(2x+7)(x+3)
(2x+7)(x+3)

(2x+1)(2x+3)
(2x+1)(2x+3)

(2x+1)(x+3)

Answer 1

To factor the quadratic expression \(2x^2 + 7x + 3\), we can use the method of factoring by grouping or finding two numbers that multiply to \(2 \times 3 = 6\) and add up to \(7\).

The factors of \(6\) that add up to \(7\) are \(6\) and \(1\).

So, we can rewrite the quadratic as follows:

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

Next, we can group the terms:

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

Now, factor out the common terms from each group:

\[
2x(x + 3) + 1(x + 3)
\]

Now we can factor out the common binomial factor:

\[
(2x + 1)(x + 3)
\]

Thus, the factored form of the quadratic expression \(2x^2 + 7x + 3\) is:

\[
(2x + 1)(x + 3)
\]

Therefore, the correct response is:

**(2x+1)(x+3)**