5.8 polynomial equations - solving equations by factoring

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5.8 Polynomial Equations - Solving Equations by Factoring. Solutions to Equations in One Variable: Where the curve crosses the x-Axis (if it does!) Solving Quadratic Equations ax 2 + bx + c = 0 Zero factor property Solving Higher Degree Equations Problem Solving - PowerPoint PPT Presentation

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Sect. 2.2

5.8 Polynomial Equations - Solving Equations by FactoringSolutions to Equations in One Variable:Where the curve crosses the x-Axis (if it does!)Solving Quadratic Equationsax2 + bx + c = 0Zero factor propertySolving Higher Degree EquationsProblem SolvingNot covered:Functions/Graphs

5.81Curves and x-Interceptsy=x+3 y=x2 y=x3 y=|x|

5.82Definition

Zero Factor Property

5.83

Solving a Quadratic Equation by Factoring5.84

Examples: 0, 1, or 2 solutionsRewriteFactorSet Each = 0Solve EachCheckUnfactorable quadratics are prime and have no rational number solutions.5.85

Practice: 0, 1, or 2 solutionsRewriteFactorSet Each = 0Solve EachCheckUnfactorable quadratics are prime and have no rational number solutions.5.86Higher Degree Polynomial EquationsWrite in descending powers of the variable = 0Make leading coefficient positive (multiply by -1)FactorSolve each factor = 0May have 0 to n (the degree) solutionsCheck all solutions in original equation5.87

Examples, 0 to n solutionsRewriteFactorSet Each = 0Solve EachCheckUnfactorable quadratics are prime and have no rational number solutions.

5.88

Practice, 0 to n solutionsRewriteFactorSet Each = 0Solve EachCheckUnfactorable quadratics are prime and have no rational number solutions.

5.89IntegersConsecutive Integers: n, n+1, n+2, n+3, Consecutive Even or Odd Integers:n, n+2, n+4, n+6, Find 3 consecutive odd integers where the product of the first 2 is 68 more than the 3rd integer.

5.810

Borders

5.811Gravity

SLINGSHOT A slingshot can provide an initial velocity of 128 feet per second. At what times will a stone, shot vertically upward, be 192 feet above the ground?

5.812What Next?6.1 Rational Expressions

Look for patterns

5.813