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UNIT 2 – QUADRATIC, POLYNOMIAL, AND RADICAL EQUATIONS AND INEQUALITIES Chapter 6 – Polynomial Functions 6.3 – Dividing Polynomials

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6.3 – DIVIDING POLYNOMIALS In this section we will learn how to: Divide polynomials using long division Divide polynomials using synthetic division

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6.3 – DIVIDING POLYNOMIALS In lesson 6.1 we learned how to divide monomials We can use the same skills to divide polynomials by monomials

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6.3 – DIVIDING POLYNOMIALS Example 1 Simplify 5a 2 b – 15ab 3 + 10a 3 b 4 5ab

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6.3 – DIVIDING POLYNOMIALS You can use a process similar to long division to divide a polynomial by a polynomial with more than one term. The process is known as the division algorithm. When doing division, remember that you can only add or subtract LIKE TERMS

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6.3 – DIVIDING POLYNOMIALS Example 2 Use long division to find (x 2 – 2x – 15) ÷ (x – 5)

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6.3 – DIVIDING POLYNOMIALS Just like dividing whole numbers, dividing polynomials may result in a quotient with a remainder. Remember: 9 / 2 = 4 + R1 and is often written as 4 ½. The result of division of polynomials with a remainder can be written in a similar manner.

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6.3 – DIVIDING POLYNOMIALS Example 3 Which expression is equal to (a 2 – 5a + 3)(2 – a) -1 ? a + 3 -a + 3 - 3/(2 – a) -a – 3 + 3/(2 – a) -a + 3 + 3/(2 – a)

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6.3 – DIVIDING POLYNOMIALS Synthetic Division – a simpler process for dividing a polynomial by a monomial. Example 4: (x 3 – 4x 2 + 6x – 4) ÷ (x – 2) Write the terms of the dividend so that the degrees of the terms are in descending order. Then write just the coefficients. Write the constant r of the divisor x – r to the left. Bring down the first coefficient. Multiply the first coefficient by r. Write the product under the second coefficient. Add the product and the second coefficient. Multiply the sum by r. Write the product under the next coefficient and add. The numbers along the bottom row are the coefficients of the quotient. Start with the power of x that is one less than the degree of the dividend.

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6.3 – DIVIDING POLYNOMIALS Example 5 Use synthetic division to find (4y 4 – 5y 2 + 2y + 4) ÷ (2y – 1)

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6.3 – DIVIDING POLYNOMIALS HOMEWORK Page 329 #13 – 33 odd

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