Question

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

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-20\) (the constant term) and add up to \(8\) (the coefficient of \(x\)). Let's list the factor pairs of \(-20\): \((-1, 20)\), \((1, -20)\), \((-2, 10)\), \((2, -10)\), \((-4, 5)\), \((4, -5)\). Among these, the pair \(-2\) and \(10\) adds up to \(8\) (\(-2 + 10 = 8\)) and multiplies to \(-20\) (\(-2\times10=-20\)).

Step2: Factor the quadratic

Using the numbers we found, we can rewrite the middle term \(8x\) as \(-2x + 10x\). So the quadratic \(x^{2}+8x - 20\) becomes \(x^{2}-2x + 10x - 20\). Now, we factor by grouping. Group the first two terms and the last two terms: \((x^{2}-2x)+(10x - 20)\). Factor out the greatest common factor from each group: \(x(x - 2)+10(x - 2)\). Now, we can factor out the common binomial factor \((x - 2)\), which gives us \((x - 2)(x + 10)\).

Answer:

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