Question

factor the trinomial.
$x^2 - 11x + 28$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(28\) (the constant term) and add up to \(-11\) (the coefficient of the \(x\)-term). Let's list the factor pairs of \(28\): \(1\) and \(28\), \(2\) and \(14\), \(4\) and \(7\). Since the middle term is \(-11x\) and the constant term is positive, both numbers should be negative. Checking: \(-4 + (-7)=-11\) and \((-4)\times(-7) = 28\).

Step2: Factor the trinomial

Using the numbers \(-4\) and \(-7\), we can factor \(x^{2}-11x + 28\) as \((x - 4)(x - 7)\).

Answer:

\((x - 4)(x - 7)\)