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    5.3 5.3 Presentation Transcript

    • 5.3 Solving PolynomialEquations
    • Real Vs. Imaginary In Chapter 4, we found both real and imaginary solutions for quadratic equations. We can find both real and imaginary solutions for polynomial equations too! ◦ Remember:
    • To Solve a Polynomial Equationby Factoring:1. Set the equation = 02. Factor (Remember GCF first!)3. Apply the Zero-Product Property (Set each factor = 0 and solve for x)  If you have a quadratic that is not factorable, use the quadratic formula
    • Example: Find the real orimaginary solutions of eachequation.
    • Example: Find the real orimaginary solutions of eachequation.
    • Factoring a Sum or Difference ofCubes To factor a sum or difference of cubes, we use the following “shortcut”
    • Example: Factor
    • Factoring by Substitution Factoring by substitution is useful when you have a polynomial of degree 4 or higher and no GCF It is also useful if you have a variable in the denominator (more about this later!)
    • Solving by Factoring withSubstitution1. Write the polynomial in standard form2. Identify the piece that will be substituted3. Substitute4. Factor5. Undo the substitution6. Solve for the variable
    • Find the real or imaginarysolutions of each equation byfactoring.
    • Find the real or imaginarysolutions of each equation byfactoring.
    • Finding Real Roots byGraphing1. Write the equation in standard form2. Enter the equation into3. Use the zero feature to find all real zerosExample: Find the Real Solutions of the equation by graphing.
    • Assignment Classwork: p 301 #25 – 36 odd Homework: p 301 #11 – 23odd, 39 – 47odd, not 45