2. Long Division Just like in the 3 rd grade 6x 3 + 19x 2 + 16x – 4 divided by x - 2 x - 2 6x 3 + 19x 2 + 16x - 4

3. U-Try (4x 3 -7x 2 – 11x + 5) divided by (4x + 5)

4. Synthetic division to divide ax 3 + bx 2 + cx +d by (x – k) k a b c d a ka b-ka remainder Coefficients of Quotient k(b-ka)

5. Lets try one x 4 – 10x 2 – 2x + 4 divided by ( x + 3) ( x + 3) k = -3 -3 x 4 + 0x 3 – 10x 2 – 2x + 4 1 1 0 –10 – 2 4 -3 9 3 1 -3 1

6. x 4 + 0x 3 – 10x 2 – 2x + 4 1 1 0 –10 – 2 4 -3 9 3 1 -3 1 remainder __x 3 + __x 2 + __x + __ + __ (x + 3)

7. You try 3x 3 -17x 2 + 15x -25 divided by (x - 5)

8. Pretty Cool Remainder Theorem If a polynomial is divided by (x - k) then the remainder will be f(k) Or the PCRT

9. Let’s try one Find the remainder of the problem 9x 3 – 16x – 18x 2 + 32 divided by (x – 2) f(x) = 9x 3 – 16x – 18x 2 + 32 f(2) = 9(2) 3 – 16(2) – 18(2) 2 + 32 f(2) = 9(8) – 16(2) – 18(4) + 32

11. Is it a root? If you try synthetic division and there is no remainder, that means k is a solution to f(x) = 0 or … f(k) = 0 A great way to test for roots of higher degree polynomials

12. The most confusing instructions for any homework problem I’ve ever seen! What they want Take f(x) and divide it by (x - k) Then write (x - k) (quotient) + remainder (x-k) Page 233 problems 39 -46

13. Divide then divide again to factor 3 rd degree polynomials given 2 factors

14. Lets try a few problems Page 235 problems 7 - 15 21 - 27 51 - 65