Question

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

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-20\) (the constant term) and add up to \(-1\) (the coefficient of the \(x\)-term). Let's list the factor pairs of \(-20\): \((-5, 4)\) because \(-5\times4 = -20\) and \(-5 + 4=-1\).

Step2: Factor the quadratic

Using the numbers we found, we can factor \(x^{2}-x - 20\) as \((x - 5)(x + 4)\). We check: \((x - 5)(x + 4)=x^{2}+4x-5x - 20=x^{2}-x - 20\), which matches the original expression.

Answer:

\((x - 5)(x + 4)\)