Question

factor.
$x^2 - 15x + 26$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(26\) (the constant term) and add up to \(-15\) (the coefficient of \(x\)). Let's list the factor pairs of \(26\): \(1\) and \(26\), \(2\) and \(13\). Since the product is positive and the sum is negative, both numbers should be negative. Checking: \(-2 + (-13)=-15\) and \((-2)\times(-13) = 26\).

Step2: Factor the quadratic

Using the numbers we found, we can factor \(x^{2}-15x + 26\) as \((x - 2)(x - 13)\).

Answer:

\((x - 2)(x - 13)\)