1 / 6

Quadratics

Quadratics . Expressions. Equations. Factoring. Solve by …. Setting = zero & Factoring . Removing Common Factors. ( )( ) = 0. How do you know which one to use ?. Factoring: Puzzle Method. Extracting Square Roots. u 2 = constant. Difference of Two Squares.

erek
Download Presentation

Quadratics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Quadratics Expressions Equations Factoring Solve by … Setting = zero & Factoring Removing Common Factors ( )( ) = 0 How do you know which one to use ? Factoring: Puzzle Method Extracting Square Roots u 2 = constant Difference of Two Squares x 2+bx+ c = 0 (x + )2= Completing the Square Perfect Square Trinomials Using Quadratic Formula Sum or Difference of Two Cubes

  2. Polynomials of degrees > 2 • Objective is to get to a recognizable quadratic form & then to use one of your known tools. They are: • Factoring to a pair of binomials: (…)(…) • Extracting the Square: u2 – c = 0 • Completing the Sq: (x + )2 = • Quadratic Formula • Approaches for Polynomials of degrees > 2 : • First, factor … simple & complex  hopefully to x2 • Let x2 = u … substitute, simplify & solve P P na P

  3. Practice Problems – Simple Factoring When only Simple Factoring is Needed • 9x2+18x+81=0 • 3x2+27x+60=0 • 5x2-65x+210=0 • 2x2+10x+12=0 • 5x3+25x2+30x=0 • 2x3-4x2-48x=0 • 3x4-24x3+21x2=0 • ½x3+3x2+4x=0 • ½x3+2x2-6x=0 • ½x3+7x2+24x=0 • 2x2-162=0 • 3x3-27x=0 • 5x3-125x=0

  4. More Complex … • x4-81=0 • x4-16=0 • x5-81x=0 • 2x4-162=0 • 3x5-48x=0 • 5x5-125x=0 Win 2 Northwestern Basketball tickets 1st Hint: Let u = x2 , & substitute u for x !! 2nd Hint: See page 134 !

  5. Practice Problems – Complex Factoring When Complex Factoring is Needed • x3 – 2x2 + x – 2 = 0 • x3 – 3x2 + 2x – 6=0 • x3 – x2 + 2x – 2 = 0 • x3 + 3x2 + 4x + 12=0 • x3 – x2 – 4x + 4=0

  6. More Practice Problems What would your approach be ?? 2x3-4x2-48x=0 9x2+18x+81=0 5x5-125x=0 Make some up yourself !! Solve by ?? a) Factoring: (…)(…) b) Extracting the Square: u2 – c2 c) Completing the Sq: (x + ) 2 = d) Quadratic Formula

More Related