Question

factor as the product of two binomials.
x² + 3x − 4 =

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-4\) (the constant term) and add up to \(3\) (the coefficient of \(x\)). The numbers are \(4\) and \(-1\) because \(4\times(-1)= - 4\) and \(4+( - 1)=3\).

Step2: Factor the quadratic

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

Answer:

\((x + 4)(x - 1)\)