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Factoring Polynomials
Example 5

Example 5: Factoring Quadratics

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

Problem

Larger root of x27x18=0 is ?\text{Larger root of }x^2-7x-18=0\text{ is }?

1. Recognize Pattern

x2+bx+c=(xr1)(xr2),  r1+r2=b,  r1r2=cx^2+bx+c=(x-r_1)(x-r_2),\;r_1+r_2=-b,\;r_1r_2=c

2. Apply Method

x2+4x32=(x8)(x4)x^2+4x-32=(x--8)(x-4)

3. Conclude

x{2,9}x\in\left\{-2,9\right\}

Final answer

x{2,9}x\in\left\{-2,9\right\}