Question 23058: I need step-by-step help on solving problems such as the following.
(x^3-6x^2+7x-2) / (x-1)
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Synthetic Division is the best way to solve this. When you are dividing a polynomial by a binomial with (x- a number) or (x+ a number), take the opposite sign of what is in the binomial. In this case, since it is (x-1) use +1, and write that number down as follows, along with the coeffients of the polynomial:
+1 _| 1 -6 7 -2
____________
Start by bringing down the first coefficient which is a 1.
+1 _| 1 -6 7 -2
___________
----> 1
Multiply 1 times the +1, which gives you a 1 and place it under the -6.
+1 _| 1 -6 7 -2
______1____
----> 1
Next, you add the -6 +1, which gives you -5:
+1 _| 1 -6 7 -2
______1_____
----> 1 -5
Next, multiply the -5 times the +1, which is -5 and place it under the 7:
+1 _| 1 -6 7 -2
______1 -5___
----> 1 -5
Add the 7 + (-5), which is 2:
+1 _| 1 -6 7 -2
______1 -5__
----> 1 -5 2
Multiply 2 times +1, which is 2, and place under the -2:
+1 _| 1 -6 7 -2
______1 -5 2_
----> 1 -5 2
Add the -2 +2 which is 0 :
+1 _| 1 -6 7 -2
______1 -5 2_
----> 1 -5 2 0
The last number 0 is the remainder. The other numbers in the bottom row are the coefficients of the answer. The answer always begins with one power less than the problem was. Since the problem started with  , the answer will start with  , so the answer, with coefficients 1, -5, 2 will be  with no remainder.
That's not a great explanation. It's hard for me to explain it here. Perhaps other tutors could do better, or any standard algebra textbook might be easier to understand. Look for the topics of Long Division and Synthetic Division.
R^2 at SCC
|
|
|
