Question

Factor completely.
3m2+12m–63

Answer 1

To factor the quadratic expression \(3m^2 + 12m - 63\), we can follow these steps:

1. **Factor out the Greatest Common Factor (GCF)**:
The coefficients in the expression 3, 12, and -63 have a GCF of 3. We can factor out 3 from the expression:
\[
3(m^2 + 4m - 21)
\]

2. **Factor the quadratic expression**:
Now, we need to factor the quadratic \(m^2 + 4m - 21\). We look for two numbers that multiply to \(-21\) (the constant term) and add up to \(4\) (the coefficient of the middle term).

The numbers that satisfy these conditions are \(7\) and \(-3\):
\[
7 \times (-3) = -21 \quad \text{and} \quad 7 + (-3) = 4
\]

Therefore, we can factor \(m^2 + 4m - 21\) as:
\[
(m + 7)(m - 3)
\]

3. **Combine the factors**:
Putting this all together, we get:
\[
3(m + 7)(m - 3)
\]

So, the completely factored form of \(3m^2 + 12m - 63\) is:
\[
\boxed{3(m + 7)(m - 3)}
\]