Question

factor
$x^2 - 16x + 48$
options:
$(x - 16)(x - 3)$
$(x - 12)(x - 4)$
$(x + 6)(x - 8)$
$(x + 12)($

Explanation:

Step1: Find pair summing to -16

We need two numbers that add to $-16$ and multiply to $48$. The pair is $-12$ and $-4$, since $-12 + (-4) = -16$ and $(-12)\times(-4)=48$.

Step2: Factor the quadratic

Rewrite the quadratic using the pair, then factor by grouping:
$$x^2 -12x -4x +48 = x(x-12) -4(x-12) = (x-12)(x-4)$$

Step3: Verify the factors

Expand $(x-12)(x-4)$ to confirm:
$$(x-12)(x-4)=x^2 -4x -12x +48 = x^2 -16x +48$$

Answer:

B. $(x - 12)(x - 4)$