Skip to content
Factoring Polynomials
Lesson 3
0% complete

Lesson 3: 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+4x−21=(x−−7)(x−3)x^2+4x-21=(x--7)(x-3)

Checkpoint

Larger root of x2−9x+14=0 is ?\text{Larger root of }x^2-9x+14=0\text{ is }?

Recap

  • - Product gives constant term target.
  • - Sum gives middle coefficient target.
  • - Factored form reveals roots immediately.
Previous lessonNext lessonExamplesPracticeTry in calculator

Track progress: 0/8 completed.