Question

Factor completely.
3p2+8p–3

Answer 1

To factor the quadratic expression \(3p^2 + 8p - 3\), we can use the method of factoring by grouping.

1. **Multiply the leading coefficient and the constant term**:
\[
3 \times (-3) = -9.
\]

2. **Find two numbers that multiply to \(-9\) and add to \(8\)**:
The numbers that fit these criteria are \(9\) and \(-1\) because:
\[
9 \times (-1) = -9 \quad \text{and} \quad 9 + (-1) = 8.
\]

3. **Rewrite the middle term using these numbers**:
\[
3p^2 + 9p - 1p - 3.
\]

4. **Group the terms**:
\[
(3p^2 + 9p) + (-1p - 3).
\]

5. **Factor out the common factors from each group**:
\[
3p(p + 3) - 1(p + 3).
\]

6. **Now, factor out the common binomial factor \(p + 3\)**:
\[
(3p - 1)(p + 3).
\]

Thus, the completely factored form of \(3p^2 + 8p - 3\) is:
\[
(3p - 1)(p + 3).
\]