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

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

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

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

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

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

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

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.

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)

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.

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

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