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Factoring Polynomials
Lesson 8
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Lesson 8: Factoring Quadratics

Recognize factors from sum and product patterns.

For monic quadratics, find two numbers whose product matches the constant term and whose sum matches the x-coefficient.

Key formula

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

Worked example

x2−10x+25=(x−5)(x−5)x^2-10x+25=(x-5)(x-5)

Checkpoint

Larger root of x2−7x+6=0 is ?\text{Larger root of }x^2-7x+6=0\text{ is }?

Recap

  • - Product gives constant term target.
  • - Sum gives middle coefficient target.
  • - Factored form reveals roots immediately.
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