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Factoring Polynomials
Example 8

Example 8: Factoring Quadratics

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

Problem

Larger root of x2+4x5=0 is ?\text{Larger root of }x^2+4x-5=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+7x8=(x8)(x1)x^2+7x-8=(x--8)(x-1)

3. Conclude

x{5,1}x\in\left\{-5,1\right\}

Final answer

x{5,1}x\in\left\{-5,1\right\}