Question

factor.
$y^2 - 3y - 10$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-10\) (the constant term) and add up to \(-3\) (the coefficient of the middle term). Let's list the factor pairs of \(-10\): \((-5, 2)\) because \(-5\times2 = -10\) and \(-5 + 2=-3\).

Step2: Factor the quadratic

Using the numbers we found, we can factor the quadratic \(y^{2}-3y - 10\) as \((y - 5)(y+2)\). We check by expanding: \((y - 5)(y + 2)=y^{2}+2y-5y - 10=y^{2}-3y - 10\), which matches the original expression.

Answer:

\((y - 5)(y + 2)\)