Question

question
factor.
$x^2 + 7x + 6$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(6\) (the constant term) and add up to \(7\) (the coefficient of \(x\)). The numbers are \(1\) and \(6\) since \(1\times6 = 6\) and \(1 + 6=7\).

Step2: Factor the quadratic

Using the formula \(x^{2}+bx + c=(x + m)(x + n)\) where \(m\) and \(n\) are the two numbers we found, we substitute \(m = 1\) and \(n = 6\). So \(x^{2}+7x + 6=(x + 1)(x + 6)\).

Answer:

\((x + 1)(x + 6)\)