Question

factor.
$y^2 - y - 12$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-12\) (the constant term) and add up to \(-1\) (the coefficient of the middle term). Let's list the factor pairs of \(-12\): \((-4, 3)\) because \(-4\times3 = -12\) and \(-4 + 3=-1\).

Step2: Factor the quadratic

Using the numbers we found, we can rewrite the middle term of the quadratic \(y^{2}-y - 12\) as \(y^{2}-4y+3y - 12\). Then, we group the terms: \((y^{2}-4y)+(3y - 12)\). Factor out the greatest common factor from each group: \(y(y - 4)+3(y - 4)\). Now, we can factor out the common binomial factor \((y - 4)\) to get \((y - 4)(y + 3)\).

Answer:

\((y - 4)(y + 3)\)