Example 7: Factoring Quadratics

Factoring Polynomials

Example 7

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

Problem

\text{Larger root of }x^2-49=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^2-15x+54=(x-6)(x-9)

3. Conclude

x\in\left\{7,-7\right\}

Final answer

x\in\left\{7,-7\right\}