Question

Factor completely.
3f2+33f–78

Answer 1

To factor the quadratic expression \( 3f^2 + 33f - 78 \), we can follow these steps:

1. **Factor out the greatest common factor (GCF)**:
The GCF of the coefficients \(3\), \(33\), and \(-78\) is \(3\). Thus, we can factor out \(3\):

\[
3(f^2 + 11f - 26)
\]

2. **Factor the quadratic \(f^2 + 11f - 26\)**:
We need to find two numbers that multiply to \(-26\) (the constant term) and add to \(11\) (the coefficient of \(f\)).

The two numbers that work are \(13\) and \(-2\) since:
\[
13 \times (-2) = -26 \quad \text{and} \quad 13 + (-2) = 11
\]

3. **Rewrite and factor**:
Using these numbers, we can rewrite the quadratic:
\[
f^2 + 11f - 26 = (f + 13)(f - 2)
\]

4. **Combine everything**:
Therefore, inserting this factorization back into our expression gives:
\[
3(f + 13)(f - 2)
\]

So, the complete factorization of \(3f^2 + 33f - 78\) is:

\[
\boxed{3(f + 13)(f - 2)}
\]