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

Answer 1

To factor the quadratic expression \(2x^2 + 7x + 3\), we look for two numbers that multiply to \(2 \cdot 3 = 6\) (the product of the leading coefficient and the constant term) and add to \(7\) (the coefficient of the middle term).

The numbers \(6\) and \(1\) fit this requirement because:
- \(6 \times 1 = 6\)
- \(6 + 1 = 7\)

Next, we can rewrite the middle term of the quadratic expression using these numbers:
\[
2x^2 + 6x + 1x + 3
\]

Now, we can group the terms:
\[
(2x^2 + 6x) + (1x + 3)
\]

We can factor out the common terms in each group:
\[
2x(x + 3) + 1(x + 3)
\]

Now, we notice that \((x + 3)\) is a common factor:
\[
(2x + 1)(x + 3)
\]

Thus, the factored form of the quadratic expression \(2x^2 + 7x + 3\) is:
\[
(2x + 1)(x + 3)
\]

So the correct answer from the options provided is:
\((2x + 1)(x + 3)\).