Lesson 8 of 8

Factoring & Intro to Quadratics

Factoring is the reverse of multiplying. You take a polynomial like x^2 + 5x + 6 and break it back into two binomials that multiply to give it.

  1. 1Factor x^2 + 5x + 6
  2. 2Find two numbers that MULTIPLY to 6 and ADD to 5
  3. 3Those numbers are 2 and 3 (2 times 3 = 6, 2 + 3 = 5)
  4. 4Write it as (x + 2)(x + 3)

The zero-product idea

If two things multiply to zero, then at least one of them must be zero. So if (x + 2)(x + 3) = 0, then x + 2 = 0 or x + 3 = 0, giving x = -2 or x = -3. Those are the solutions of the quadratic.

ON THE TEST

Set the equation equal to 0 first, then factor, then set each factor to 0 and solve. A quadratic usually has two answers.

A quadratic equation (one with an x^2 term) graphs as a U-shaped curve called a parabola. It opens up if the x^2 term is positive and opens down if it's negative. The points where the parabola crosses the x-axis are the solutions you found by factoring.

Coach Fite

Factoring trips people up because it feels like guessing. It's not. Find the two numbers that multiply and add right, every time. Run it til it's automatic, same as footwork. Pass this unit and you've basically finished the year.

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