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Factor the trinomial completely.

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

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

1 answer

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:

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