Question

Which expression is equivalent to the trinomial?
9x^2 - 9x - 4
type your answers to each problem in the table below. The order does not matter

Answer 1

To factor the trinomial \(9x^2 - 9x - 4\), we can look for two numbers that multiply to \(a \cdot c = 9 \cdot (-4) = -36\) and add to \(b = -9\).

1. **Identify \(a\), \(b\), and \(c\):**
- \(a = 9\)
- \(b = -9\)
- \(c = -4\)

2. **Factors of \(-36\):**
- The pairs of factors that multiply to \(-36\) include:
- (1, -36)
- (2, -18)
- (3, -12)
- (4, -9)
- (6, -6)
- (-1, 36)
- (-2, 18)
- (-3, 12)
- (-4, 9)
- (-6, 6)

3. **Finding the correct pair:**
- Among these pairs, the pair that adds to \(-9\) is \(3\) and \(-12\):

4. **Rewrite the trinomial:**
\[
9x^2 + 3x - 12x - 4
\]

5. **Group the terms:**
\[
(9x^2 + 3x) + (-12x - 4)
\]

6. **Factor each group:**
\[
3x(3x + 1) - 4(3x + 1)
\]

7. **Factor out the common binomial:**
\[
(3x + 1)(3x - 4)
\]

Thus, the expression \(9x^2 - 9x - 4\) is equivalent to \((3x + 1)(3x - 4)\).

So the final answer is:
\[
\boxed{(3x + 1)(3x - 4)}
\]