5.2 Solving Quadratic Equations by Factoring

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Presentation transcript:

5.2 Solving Quadratic Equations by Factoring

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

Practice Problems

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

Practice Problems:

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

Practice problems:

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

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

Practice Problems: Solving Quadratic Equations:

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?

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