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Factoring Polynomials
Example 11

Example 11: Factoring Quadratics

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

Problem

Larger root of x25x24=0 is ?\text{Larger root of }x^2-5x-24=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

x217x+72=(x9)(x8)x^2-17x+72=(x-9)(x-8)

3. Conclude

x{8,3}x\in\left\{8,-3\right\}

Final answer

x{8,3}x\in\left\{8,-3\right\}