Example 4: Factoring Quadratics

Factoring Polynomials

Example 4

Step-by-step worked example for this lesson track.

Problem

\text{Larger root of }x^2+15x+54=0\text{ is }?

1. Recognize Pattern

x^2+bx+c=(x-r_1)(x-r_2),\;r_1+r_2=-b,\;r_1r_2=c

2. Apply Method

x^2-5x-50=(x-10)(x--5)

3. Conclude

x\in\left\{-6,-9\right\}

Final answer

x\in\left\{-6,-9\right\}