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Unit 2 – quadratic, polynomial, and radical equations and inequalities

Unit 2 – quadratic, polynomial, and radical equations and inequalities. Chapter 6 – Polynomial Functions 6.6 – Solving Polynomial Equations. 6.6 – Solving Polynomial Equations. In this section we will learn how to: Factor polynomials Solve polynomial equations by factoring.

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Unit 2 – quadratic, polynomial, and radical equations and inequalities

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  1. Unit 2 – quadratic, polynomial, and radical equations and inequalities Chapter 6 – Polynomial Functions 6.6 – Solving Polynomial Equations

  2. 6.6 – Solving Polynomial Equations • In this section we will learn how to: • Factor polynomials • Solve polynomial equations by factoring

  3. 6.6 – Solving Polynomial Equations • Whole numbers are factored using prime numbers • 100 = 2 • 2 • 5 • 5 • Many polynomials can also be factored. • Their factors are other polynomials • Polynomials that cannot be factored are called prime

  4. 6.6 – Solving Polynomial Equations

  5. 6.6 – Solving Polynomial Equations • Whenever you factor a polynomial, ALWAYS LOOK FOR A COMMON FACTOR FIRST • Then determine whether the resulting polynomial factor can be factored again using one or more of the methods

  6. 6.6 – Solving Polynomial Equations • Example 1 • Factor 10a3b2 + 15a2b – 5ab3

  7. 6.6 – Solving Polynomial Equations • Example 2 • Factor x3 + 5x2 – 2x – 10

  8. 6.6 – Solving Polynomial Equations • Factoring by grouping is the only method that can be used to factor polynomials with four or more terms • For polynomials with two or three terms, it may be possible to factor the polynomial using the chart

  9. 6.6 – Solving Polynomial Equations • Example 3 • Factor each polynomial • 12y3 – 8y2 – 20y • 64x6 – y6

  10. 6.6 – Solving Polynomial Equations • In some cases you can rewrite a polynomial in x in the form au2 + bu + c • By letting u = x2 the expression x4 – 16x2 + 60 can be written as (x2)2 – 16(x2) + 60 = u2 – 16u + 60 • This new (but equivalent) expression is said o be in quadratic form

  11. 6.6 – Solving Polynomial Equations • An expression that is quadratic in form can be written as au2 + bu + c for any numbers a, b, and c, a ≠ 0, where u is some expression in x. The expression au2 + bu + c is called the quadratic form of the original expression

  12. 6.6 – Solving Polynomial Equations • Example 4 • Write each expression in quadratic form, if possible • 2x6 – x3 + 9 • x4 – 2x3 – 1

  13. 6.6 – Solving Polynomial Equations • In Chapter 5 we learned to solve quadratic equations by factoring and using the Zero Product Property. • You can extend these techniques to solve higher-degree polynomial equations

  14. 6.6 – Solving Polynomial Equations • Example 5 • Solve each equation • x3 – 216 = 0 • x4 – 29x2 + 100 = 0

  15. 6.6 – Solving Polynomial Equations HOMEWORK Page 353 #15 – 35 odd, 36 – 38 all

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