1. Long Division Synthetic Division Remainder Theorem Can only divide by x-a

2. Long Division: Divide Factor x2x2 Subtract by adding the opposite 0 + 0 - 2x - 1 0 + 0 -2x + 3 0 Is 3/2 a root? Yes because there was no remainder!

3. Long Division: Divide Factor x Subtract by adding the opposite -5x - 5 - 2 + -5x - 20 18 Is -4 a root? No because there was a remainder!

4. Synthetic Division: Divide Root 2 3 -4 15 -3 2 -6 Is -3 a root? Yes because there was no remainder! -3 9 5 0 -15

5. Synthetic Division: Divide Root 3 -4 2 -1 3 -3 Is -1 a root? No because there was a remainder! -7 7 9 -10 -9

6. Remainder Theorem 1 0 -5 4 12 -4 1 Find f(-4) Notice f(-4) = the remainder above!!!!! -4 16 11 -40 -44 160 172

7. Remainder Theorem 2 6 -5 0 -61 2 -2 Find P(-1) You can find P(-1) using synth div or substitution 4 -4 -9 9 9 -70

8. 1 2 -11 -12 1 Factor Now If you can’t factor then QF or compl the square! 1 -12 12 0 Not factorable Divide by -1 using synthetic division Multiply Add To Notes!

9. 1 4 -3 -2 1 1 1 You can’t factor so QF or complete the square! 5 5 2 2 0 Not factorable Divide by 1 using synthetic division Multiply Add To Notes!