1. 6-3: D IVIDING P OLYNOMIALS Essential Question: What does the last number in the bottom line of synthetic division represent?

2. 6-3: D IVIDING P OLYNOMIALS Using Long Division Polynomial Long division works similarly to regular long division (I know… it’s been a while) Divide 1,732,042 by 440 Answer is 3936, R: 202

3. 6-3: D IVIDING P OLYNOMIALS Divide x 2 + 3x – 12 by x – 3 Answer is x + 6, R: 6

4. 6-3: D IVIDING P OLYNOMIALS Y OUR T URN Divide x 2 – 3x + 1 by x – 4 Answer is x + 1, R: 5

5. 6-3: D IVIDING P OLYNOMIALS We can use division to find factors of a polynomial. If the remainder of division comes out to be 0, then the divisor (and quotient) are factors. Determine whether x + 4 is a factor of the polynomial x 2 + 6x + 8. Because the remainder is 0, x + 4 IS a factor of x 2 + 6x + 8 (so is x + 2)

6. 6-3: D IVIDING P OLYNOMIALS Determine whether x + 4 is a factor of the polynomial x 3 + 3x 2 – 6x – 7. Because the remainder is not 0, x + 4 IS NOT a factor of x 3 + 3x 2 – 6x – 7

7. 6-3: D IVIDING P OLYNOMIALS Y OUR T URN Determine whether x – 8 is a factor of the polynomial 2x 2 – 19x + 24. Because the remainder is 0, x – 8 IS a factor of 2x 2 – 19x + 24

8. 6-3: D IVIDING P OLYNOMIALS Y OUR T URN Determine whether x + 2 is a factor of the polynomial x 3 – 4x 2 + 3x +2. Because the remainder is not 0, x + 2 IS NOT a factor of x 3 – 4x 2 + 3x + 2

9. 6-3: D IVIDING P OLYNOMIALS Assignment Page 324 Problems 1 – 12 (all problems) Obviously, show your work Tomorrow Quiz review Next week The secrets of synthetic division Chapter 6 Test

10. U NIT #4: P OLYNOMIALS 6-3: D IVIDING P OLYNOMIALS D AY 2 Essential Question: What does the last number in the bottom line of synthetic division represent?

11. 6-3: D IVIDING P OLYNOMIALS Synthetic Division Can only be used when the divisor is “x” +/- some constant (e.g. “x + 2”, “x – 10”) Step 1: Reverse the sign of the constant terms in the divisor. Write the coefficients of the polynomial in standard form. Step 2: Bring down the first coefficient Step 3: Multiply the first coefficient by the new divisor. Write the result under the next coefficient. Add. Step 4: Repeat the steps of multiplying and adding until the remainder is found. Step 5: The quotient begins one degree less than the dividend.

12. 6-3: D IVIDING P OLYNOMIALS Divide 3x 3 – 4x 2 + 2x – 1 by x + 1

13. 6-3: D IVIDING P OLYNOMIALS Divide 3x 3 – 4x 2 + 2x – 1 by x + 1

14. 6-3: D IVIDING P OLYNOMIALS Divide 3x 3 – 4x 2 + 2x – 1 by x + 1

15. 6-3: D IVIDING P OLYNOMIALS Divide 3x 3 – 4x 2 + 2x – 1 by x + 1

16. 6-3: D IVIDING P OLYNOMIALS Divide 3x 3 – 4x 2 + 2x – 1 by x + 1 The quotient is 3x 2 – 7x + 9, R: -10

17. 6-3: D IVIDING P OLYNOMIALS Y OUR T URN Divide x 3 – 4x 2 + x – 6 by x – 3 Answer is x 2 – 1x – 2, R: -12

18. 6-3: D IVIDING P OLYNOMIALS Assignment Page 324 – 325 Problems 13 – 22 & 48 – 51 (all problems) Obviously, show your work Tomorrow Chapter 6 Review Packet will be distributed