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Chapter 10 Polynomials and Factoring

Chapter 10 Polynomials and Factoring. 1, 2, 3 Come Factor With Me!. Section 10.1 Adding and Subtracting Polynomials. Prior Knowledge: In your textbook review page 100 and page 451 LOOK BACK Distributive Property:.

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Chapter 10 Polynomials and Factoring

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  1. Chapter 10 Polynomials and Factoring 1, 2, 3 Come Factor With Me!

  2. Section 10.1 Adding and Subtracting Polynomials Prior Knowledge: In your textbook review page 100 and page 451 LOOK BACK Distributive Property: Add exponents when variables are the same and raised to the same power. Multiply powers when you have a power raised to a power. Only like terms can be added or subtracted, but unlike terms can be multiplied or divided.

  3. Starter Identify the leading coefficient; then classify the polynomial by degree and number of terms. 1. 2. Add or Subtract 3. 4. 5. 6.

  4. One more time: Section 10.2 Multiplying Polynomials Foil (First, Outer, Inner, Last) Example 1: Use distributive property twice Example 2: Product of the first terms + Product of the last terms+ Product of Inner terms + Product of Last Terms Now simplify:

  5. In lesson 10.2 you can always use FOIL to multiply two binomials. Some pairs of binomials have special products. You need to recognize these pairs to make finding products easier and faster. • Sum and Difference Pattern – Some books refer to this as the Difference of Two Squares Example:

  6. Section 10.3 Special Products of Polynomials Square of a binomial Pattern Example 1: Example 2:

  7. Reminder: Standard Form is Related Equation A polynomial is in factored form if it is written as the product of two or more linear factors. Factored form: Standard form of a quadratic equation:

  8. Example 1: Use Zero-Product Property Solve each linear product for x by setting each linear equation product to equal 0 (because when y is 0 in your ordered pair you are solving for the x root of the quadratic) Example: Example 2: What does this say about how many x –intercepts there are for this quadratic?

  9. Example 3: Factor a Cubic Equation What would the original cubic equation be written in standard form? Solving Polynomial Equations in Factored Form 10.4

  10. To factor a quadratic means to write it as the product of two linear expressions. • All of the quadratic trinomials in this lesson have a leading coefficient of 1. • Remember: From FOIL

  11. Patterns!!!!! They are everywhere!!!! Example 1: Factoring when b and c are POSITIVE . Factor: What two factors can I add to get 8 but multiply together to get 15? • Multiply to check your answer!!!!

  12. Example 2: Factoring when b is negativeand c is positive Factor:What two factors will give me a sum of -9 and when I multiply those same factors will give me a product of +20? Factored products: Example 3: Factoring when b and c are negative Factored : What two factors can I add together that will give me -8 and when I multiply the same factors will give me a product of -9?

  13. Example 4: Factoring when b is positive and c is negative. What factors will give me a sum of 3 and a product of -18? Factored linear products: • Many quadratic trinomials with integer coefficients cannot be factored into linear factors. • Itcanbe factored if the discriminant is a perfect square. A. B.

  14. Factoring Section 10.5 • Write the equation • Write in standard form and set the equation to 0. • Factor into linear products (example 3). Ask yourself what two factors will add to -5 and the same two factors can be multiplied to give a product of -24? • 4. Set each linear product to zero and solve for the x-intercept or roots of the quadratic equation. Example 5: Solving a Quadratic Equation

  15. Factoring Section 10.6 In this lesson you will factor a quadratic polynomials whose leading co-efficient is not 1 ! Example 1: One pair of factors for a and c. Example 2: One pair of factors for a and c.

  16. In section 10.3 you factored special products. In this section, there are two forms of a perfect square trinomial. • Difference of two squares • Perfect Square Trinomial • Example:

  17. Example: Example: Multiplying by 4 allows you to eliminate the fraction. Factoring Special Products Section 10.7

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