Question

question
factor.
$x^2 - 3x - 28$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to $-28$ (the constant term) and add up to $-3$ (the coefficient of the $x$ term). Let's list the factor pairs of $28$: $(1,28)$, $(2,14)$, $(4,7)$. We need one positive and one negative number since their product is negative. The pair $4$ and $-7$ works because $4\times(-7)=-28$ and $4 + (-7)=-3$.

Step2: Factor the quadratic

Using the two numbers we found, we can factor the quadratic $x^2 - 3x - 28$ as $(x + 4)(x - 7)$ because when we expand $(x + 4)(x - 7)$ using the distributive property (FOIL method), we get $x^2 - 7x + 4x - 28 = x^2 - 3x - 28$, which matches the original expression.

Answer:

$(x + 4)(x - 7)$