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Polynomials and Polynomial Functions

Chapter 5. Polynomials and Polynomial Functions. Chapter Sections. 5.1 – Addition and Subtraction of Polynomials 5.2 – Multiplication of Polynomials 5.3 – Division of Polynomials and Synthetic Division 5.4 – Factoring a Monomial from a Polynomial and Factoring by Grouping

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Polynomials and Polynomial Functions

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  1. Chapter 5 Polynomials and Polynomial Functions

  2. Chapter Sections 5.1 – Addition and Subtraction of Polynomials 5.2 – Multiplication of Polynomials 5.3 – Division of Polynomials and Synthetic Division 5.4 – Factoring a Monomial from a Polynomial and Factoring by Grouping 5.5 – Factoring Trinomials 5.6 – Special Factoring Formulas 5.7-A General Review of Factoring 5.8 - Polynomial Equations

  3. Division of Polynomials and Synthetic Division § 5.3

  4. Divide a Polynomial by a Monomial To Divide a Polynomial by a Monomial Divide each term of the polynomial. To divide a polynomial by a monomial, we will need to use the quotient rule for exponents, the zero exponent rule, and the negative exponent rule.

  5. Divide a Polynomial by a Monomial Example

  6. dividend divisor 3t 1. Divide 6t 2 by 2t. Write the quotient above the term containing the t. 6t2 + 15t 2. Multiply the 3t by 2t + 5. Write the product under the like terms. -16t - 40 3. Subtract. Bring down the remaining term. Dividing Polynomials To divide a polynomial by a polynomial, use the same method as when performing long division.

  7. 3t - 8 6t2 +15t -16t - 40 4. Repeat, using the first term in the bottom row: -16t 2t = - 8 -16t- 40 0 Check your answer using the FOIL method. Dividing Polynomials

  8. Use the Remainder Theorem Remainder Theorem If the polynomial P(x) is divided by x – a, the remainder is equal to P(a).

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