Question

2p^2+7p+3. Factor

Answer 1

To factor the quadratic expression \(2p^2 + 7p + 3\), we need to find two numbers that multiply to \(2 \cdot 3 = 6\) (the product of the coefficient of \(p^2\) and the constant term) and add up to \(7\) (the coefficient of \(p\)).

The numbers that satisfy these conditions are \(6\) and \(1\) because:

- \(6 \times 1 = 6\)
- \(6 + 1 = 7\)

Now we can rewrite the middle term \(7p\) using these two numbers:

\[
2p^2 + 6p + 1p + 3
\]

Next, we can factor by grouping:

\[
(2p^2 + 6p) + (1p + 3)
\]

Now, factor out the common factors in each group:

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

Now we can factor out the common binomial factor \((p + 3)\):

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

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

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