1. 5.2 Solving Quadratic Equations by Factoring

2. Terminology Binomials- expressions having 2 terms
Examples: x+2 and 2x2-5x
Trinomial- expressions having 3 terms
Examples: x2 + 2x + 7
Factoring- used to write a trinomial as a product of binomials

3. Practice Problems

4. Special Factoring Patterns:
Pattern Name
Pattern
Example
Difference of
two Squares
a2-b2 = (a+b)(a-b)
x2-9 = (x+3)(x-3)
Perfect Square
Trinomial
a2+2ab+b2 = (a+b)2
a2-2ab+b2 = (a-b)2
x2+12x+36 = (x+6)2
x2-8x+16 = (x-4)2

5. Practice Problems:

6. Factoring… Monomial- expressions having only one term
Example: 5; and x2; and 2x
Factor out monomials first!

7. Practice problems:

8. More Terminology:
Quadratic Equation- one variable written in the form ax2+bx+c=0
Also called standard form for quadratics

9. Zero Product Property
Let A and B be real numbers or algebraic expressions. If AB=0 then A=0 or B=0

10. Practice Problems:
Solving Quadratic Equations:

11. Practice Problems:
A painter is making a rectangular canvas for her next painting. She wants the length of the canvas to be 4 feet more than twice the width of the canvas. The area of the canvas must be 30 square feet. What should the dimensions of the canvas be?

12. Finding Zeros Zeros- the functions values when y=0 X-intercepts
Examples: