Which expression is equivalent to the trinomial?

Question

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: \[ \boxed{(3x + 1)(3x - 4)} \]