Question

question
factor.
$x^2 - 8x - 20$

Explanation:

Step1: Identify factors of -20

We need two numbers that multiply to -20 and add to -8. Let's list factor pairs of -20: (1, -20), (2, -10), (4, -5), (-1, 20), (-2, 10), (-4, 5). The pair 2 and -10: \(2\times(-10)=-20\) and \(2 + (-10)=-8\).

Step2: Factor the quadratic

Using these numbers, we can write the quadratic as \((x + 2)(x - 10)\) because when we expand \((x + 2)(x - 10)\), we get \(x^{2}-10x + 2x - 20=x^{2}-8x - 20\), which matches the original expression.

Answer:

\((x + 2)(x - 10)\)