1. 7/14/2015 12:41 AM6.4 - Dividing Polynomials (Long Division)1 Polynomial Division SECTION 6.4 LONG DIVISION and Synthetic Division

2. 7/14/2015 12:41 AM 6.4 - Dividing Polynomials (Long Division)2 The methods In this section, we will look at two methods to divide polynomials:In this section, we will look at two methods to divide polynomials: –long division (similar to arithmetic long division) –synthetic division (a quicker, short-hand method) Steps for Long DivisionSteps for Long Division –Multiply the answer by the divisor and then subtract Subtracting involves multiplying by -1Subtracting involves multiplying by -1 –Repeat process until it can not be done –Leftover is remainder (Just like division)

3. 7/14/2015 12:41 AM 6.4 - Dividing Polynomials (Long Division)3 Example 1 Divide (x 2 – 5x + 4) ÷ (x – 1)Divide (x 2 – 5x + 4) ÷ (x – 1) Rewrite in long division form...

4. 7/14/2015 12:41 AM 6.4 - Dividing Polynomials (Long Division)4 Example 2 Divide (x 3 – 28x – 48) ÷ (x + 4)Divide (x 3 – 28x – 48) ÷ (x + 4)

5. 7/14/2015 12:41 AM 6.4 - Dividing Polynomials (Long Division)5 Example 3 Divide (2x 2 + 3x – 4) ÷ (x – 2)Divide (2x 2 + 3x – 4) ÷ (x – 2) Rewrite in long division form...

6. 7/14/2015 12:41 AM 6.4 - Dividing Polynomials (Long Division)6 Example 4 Divide (x 3 – 6) ÷ (x – 1)Divide (x 3 – 6) ÷ (x – 1)

7. 7/14/2015 12:41 AM 6.4 - Dividing Polynomials (Long Division)7 Example 5 Divide (12x 4 - 5x 2 – 3) ÷ (3x 2 + 1)Divide (12x 4 - 5x 2 – 3) ÷ (3x 2 + 1) Rewrite in long division form...

8. 7/14/2015 12:41 AM 6.3 Polynomials and Polynomial Functions H 8 Synthetic Division Synthetic Division allows omitting all variables and exponents

9. 7/14/2015 12:41 AM9.4 Polynomials and Polynomial Functions H 9 Steps Steps for Synthetic Division: 1.Identify the divisor and reverse the sign of the constant term. Write the coefficients of the polynomial in standard form. 2.Bring down the first coefficient 3.Multiply the first coefficient by the new divisor, identify the result under the next coefficient and add. 4.Repeat the steps of multiplying and adding until the remainder is found 5.Go backwards from the remainder and assign variables

10. 7/14/2015 12:41 AM 6.3 Polynomials and Polynomial Functions H 10 Example 1 Divide (x 3 – 13x + 12) ÷ (x + 4) by synthetic div.

11. 7/14/2015 12:41 AM 6.3 Polynomials and Polynomial Functions H 11 Example 1 Divide (x 3 – 13x + 12) ÷ (x + 4) –4 · 1 = –4 –4 · –4 = 16 –4 · 3 = –12

12. 7/14/2015 12:41 AM 6.3 Polynomials and Polynomial Functions H 12 Example 1 Divide (x 3 – 13x + 12) ÷ (x + 4)

13. 7/14/2015 12:41 AM9.4 Polynomials and Polynomial Functions H 13 Example 2 Divide (x 3 – 2x 2 – 5x + 6) ÷ (x + 2) using synthetic division

14. 7/14/2015 12:41 AM9.4 Polynomials and Polynomial Functions H 14 Example 3 Divide (x 3 – 3x 2 – 5x – 25) ÷ (x – 5) using synthetic division