Question

$x^2 + 3x - 28$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-28\) and add up to \(3\). Let's list the factor pairs of \(28\): \((1, 28)\), \((2, 14)\), \((4, 7)\). Since the product is negative, one number is positive and the other is negative. We find that \(7\) and \(-4\) work because \(7\times(-4)= -28\) and \(7 + (-4)=3\).

Step2: Factor the quadratic

Using the numbers from Step 1, we can factor \(x^{2}+3x - 28\) as \((x + 7)(x - 4)\). We check by multiplying: \((x + 7)(x - 4)=x^{2}-4x + 7x - 28=x^{2}+3x - 28\), which matches the original expression.

Answer:

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