Polynomial and Synthetic Division 2.3

1. Polynomial and Synthetic Division 2.3

2. Simplify: Scrap Paper Scrap Paper Scrap Paper Rewrite as follows: Change the signs. Change the signs. Change the signs. Ask yourself…x times what gives 2x3? Now ask yourself…x times what gives 3x2? Answer…x times 2x2 gives 2x3. Answer…x times 3x gives 3x2. Now ask yourself…x times what gives -2x? Answer…x times -2 gives -2x.

3. Example: Important Stuff to Remember!! • Your exponents must go in descending order. If you are missing an exponent, put in a zero for that place. You must change signs before you add!!! Write remainders as fractions.

4. Try these:

5. Long Division of Polynomials

6. -3 Synthetic Division Getting the problem set up. First, make sure there are no skipped powers. Rewrite with zeros if necessary. Next, write just the coefficients of the dividend. 3 7 0 1 -11 Then, find out what value makes the divisor equal zero and write that number in the “box”. Finally, skip a line and draw a line.

7. x x x x -3 Getting’ it done. 3 7 0 1-11 -9 6 -18 51 -2 6 -17 40 3 1. Bring down the first number. 2. Multiply the number in the “box” by this number. 3. Place your answer under the next number. 4. Add. 5. Repeat 2-4.

8. 3 7 0 1-11 -9 6 -18 51 -2 6 -17 40 3 -3 Now what?!? Box your last number. This is your remainder. Your first variable’s exponent will be one less than the dividend’s. The remaining exponents go in descending order.

9. The Synthetic Division Shuffle and Add! and Add! and Add! and Add! Multiply, Multiply, Multiply, Multiply,

10. Try these • Divide using synthetic division

11. Synthetic Division

12. Homework • P 159-161 # 5-13 odd and 19-27 odd, 32,

13. Answers to homework

14. Con’t answers to homework

15. Day 2 • Polynomial and Synthetic Division.

17. Try this • Use synthetic division to determine whether the given values are zeros of the function.

19. Try this • Show that (x-4) is a factor of the function:

20. Homework • P159-161 #58,60,65,78,93-96