Multiple choice

The quadratic equation $y = x^{2} - 8x - 48$ can also be represented as

  1. $y = (x - 8)^{2} - 16$
  2. $y = (x - 8)^{2} + 16$
  3. $y = (x - 8)(x + 6)$
  4. $y = (x - 12) (x + 4)$
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D Correct answer
Explanation

Factorize x^2 - 8x - 48. We need two numbers that multiply to -48 and add to -8. These are -12 and 4. So (x-12)(x+4).

AI explanation

To factorize the quadratic expression y = x^2 - 8x - 48, we must find two numbers whose product is -48 and whose sum is -8. Those two numbers are -12 and 4, so the expression factors into y = (x - 12)(x + 4). This matches the factored representation.

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