1. Factoring a polynomial with repeated division

2. Problem Show that (x-2) and (x+3) area factors of f(x)=2x^4+7x^3-4x^2-27x-18

3. Step one: You use the opposite term in the first set of parenthesis to use in your first synthetic division.

4. Step 2: Set up your problem by putting theat term out side, and the other terms on the inside in order of the x’s. if there is a missing x put a zero in its place. 2 2 7 -4 -27 -18

5. Step 3: You drop the first term down and the n multiply the 2 outsides. After doing that you put it in the blank space underneath the second term. Add then repeat through the problem. 2 2 7 -4 -27 -18 2 11 18 9 0 4 22 36 18 + + + +

6. Step 4: Now take your answer and add the x’s using one less than when you started. That is your answer for the first part. 2x^3+11x^2+18x+9

7. Step 5: Do the same thing with the second set of parenthesis, only this time use your answer from step 4 inside the box. -3 2 11 18 9 2 5 3 0 -6 -15 -9 + + +

8. Step 6: Do the same thing that you did in step 4 Now Factor the trinomial 2x^2+5x+3 (2x+3) (x+1)

9. Step 7: Factor include the two original factors in your answer (2x+3) (x+1) (x-2) (x+3)

10. Step 8: Graph