Question

Factor the trinomial completely.

Ex) 2x^2 + 5x -3: ( 2x -1) (x + 3)

4) 9x^2 - 9x - 4: _____ ____

Answer 1

To factor the trinomial \( 9x^2 - 9x - 4 \), we can follow these steps:

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

2. **Multiply a and c**:
- \( a \cdot c = 9 \cdot (-4) = -36 \).

3. **Find two numbers that multiply to \( ac = -36 \) and add to \( b = -9 \)**:
- The two numbers that work are \( -12 \) and \( 3 \) because:
- \( -12 \cdot 3 = -36 \)
- \( -12 + 3 = -9 \)

4. **Rewrite the middle term using these numbers**:
\[
9x^2 - 12x + 3x - 4
\]

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

6. **Factor by grouping**:
- From the first group, factor out \( 3x \):
\[
3x(3x - 4) + 1(3x - 4)
\]

- Now, factor out the common factor \( (3x - 4) \):
\[
(3x - 4)(3x + 1)
\]

So the completely factored form of the trinomial \( 9x^2 - 9x - 4 \) is:

\[
(3x - 4)(3x + 1)
\]