Pre-Calculus 11 Notes

By: Gen L.

In partnership with Hyperion University, 2023

Lesson 3: Solving Quadratics - Factoring

Intro

  • When solving quadratics using the factoring method, you must factor the equation.
  • There are many methods of factoring: Product/Sum, Difference of Squares, Perfect Square Trinomial, Decomposition. There is a new method known as "Substitution".

Example 1: Standard

  • Solve
    • To Solve: set each factor to 0

Example 2: GCF + Standard

  • Find the roots of

Example 3: Decomposition

  • Find the zeros of

Example 4: Difference of Squares

  • Solve

Substution Method of Factoring

  • If were asked to solve the following: , rather than working through with the binomial, we can use a placeholder.
  • Then, we solve by factoring, and replace the place holder with the binomial.

Example: Substitution

  • Solve .
  1. Substitute.
    • let
  2. Factor.
  3. Resubstitute.

Example, cont:

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