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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.

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Quadratics

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  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

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