Question

Factor the expression completely.
3x2–14x–24

please?

Answer 1

To factor the quadratic expression \( 3x^2 - 14x - 24 \), we can follow these steps:

1. **Identify the coefficients**: In the expression \( ax^2 + bx + c \):
- \( a = 3 \)
- \( b = -14 \)
- \( c = -24 \)

2. **Multiply \( a \) and \( c \)**:
\[
ac = 3 \times (-24) = -72
\]

3. **Find two numbers that multiply to \( ac \) and add to \( b \)**: We need two numbers that multiply to \(-72\) and add up to \(-14\). The numbers \(-18\) and \(4\) work:
- \(-18 + 4 = -14\)
- \(-18 \times 4 = -72\)

4. **Rewrite the middle term using these numbers**:
\[
3x^2 - 18x + 4x - 24
\]

5. **Factor by grouping**:
- Group the first two terms and the last two terms:
\[
(3x^2 - 18x) + (4x - 24)
\]
- Factor out common factors in each group:
\[
3x(x - 6) + 4(x - 6)
\]

6. **Factor out the common binomial**:
\[
(3x + 4)(x - 6)
\]

So, the completely factored form of the expression \( 3x^2 - 14x - 24 \) is:
\[
\boxed{(3x + 4)(x - 6)}
\]