Question

factor $x^2 + 8x + 7$. the factored expression is $\square$.

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(7\) (the constant term) and add up to \(8\) (the coefficient of \(x\)). The numbers \(1\) and \(7\) work because \(1\times7 = 7\) and \(1 + 7=8\).

Step2: Factor the quadratic

Using the two numbers found, we can factor the quadratic \(x^{2}+8x + 7\) as \((x + 1)(x + 7)\).

Answer:

\((x + 1)(x + 7)\)