Question

factor the following expression.
x² + 9x + 8
x² + 9x + 8 = □

Explanation:

Step1: Find two numbers

We need two numbers that multiply to 8 (the constant term) and add up to 9 (the coefficient of x). The numbers are 8 and 1 since \(8\times1 = 8\) and \(8 + 1=9\).

Step2: Factor the quadratic

For a quadratic of the form \(ax^{2}+bx + c\) (here \(a = 1\), \(b=9\), \(c = 8\)), we can write it as \((x + m)(x + n)\) where \(m\) and \(n\) are the two - found numbers. So \(x^{2}+9x + 8=(x + 8)(x+1)\).

Answer:

\((x + 8)(x + 1)\)