Question

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

Explanation:

Step1: Find two numbers

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

Step2: Factor the quadratic

Using the numbers we found, we can factor the quadratic \(y^2 + 8y - 20\) as \((y - 2)(y + 10)\). We check this by expanding: \((y - 2)(y + 10) = y^2 + 10y - 2y - 20 = y^2 + 8y - 20\), which matches the original expression.

Answer:

\((y - 2)(y + 10)\)