Slide 1

Factoring a polynomial with
repeated division


Slide 2

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


Slide 3

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


Slide 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


Slide 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
+ +
+
+
4 22 36 18

2 11 18 9

0


Slide 6

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

• That is your answer for the first part.


Slide 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
+ +
+
-6 -15 -9
2

5

3

0


Slide 8

Step 6:
• Do the same thing that you did in step 4

2x^2+5x+3

• Now Factor the trinomial
(2x+3) (x+1)


Slide 9

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


Slide 10

Step 8:
• Graph