Question

question
factor.
$x^2 - 13x + 30$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(30\) (the constant term) and add up to \(-13\) (the coefficient of \(x\)). The numbers are \(-10\) and \(-3\) since \((-10)\times(-3) = 30\) and \((-10)+(-3)=-13\).

Step2: Factor the quadratic

Using the numbers found, we can factor the quadratic as \((x - 10)(x - 3)\) because \(x^{2}-13x + 30=(x-10)(x - 3)\).

Answer:

\((x - 10)(x - 3)\)