+129852 (20x^4 + 5x^3 - 10x^2 + 30x)
________________________
5x
Note, Katie, that we can break this up as:
20x^4 / 5x + 5x^3 / 5x - 10x^2 / 5x + 30x / 5x =
4x^3 + x^2 - 2x + 6
+545 okay thank you CPhill is this the same when you have a number such as say the same number but instead of deviding it by 5x it's devided by (2+x)?
+129852 In this case, Katie, it was easy to split up the terms and divide them individually since the denominator was only one term.......this may not always work so well it we were dividing by more than one term [such as x + 2 ]
Another approach is to see if we could factor the top.....this is usually preferable...sometimes, we get a factor that "cancels" with the denominator with this method.....let's try it that way :
(20x^4 + 5x^3 - 10x^2 + 30x) = 5x ( 4x^3 + x^2 - 2x + 6)
5x 5x
Note that, now.......the "5x's" would "cancel" and we would be left with my original answer.......this "factor and cancel" method is usually good to try when we're dividing by more than one term......!!!!!
Of course....polynomial "long division" would always give us the correct answer......[there may be a remainder, in some cases, though ]
Does that help ???
+545 not really I don't think you got the question. let me give you the problem maybe you could explain it better if I showed you what I mean
(x^3 - 3x^2 + 2x + 5)
(x + 2)
+129852 (x^3 - 3x^2 + 2x + 5)
(x + 2)
Here....I can't tell if the top is factorable, or not.....polynomial long division is the method that would work the best...
( x^2 - 5x + 12 )
x + 2 [ x^3 - 3x^2 + 2x + 5 ]
x^3 + 2x^2
----------------------------
-5x^2 + 2x
-5x^2 -10x
-----------------
12x + 5
12x + 24
------------
-19
So......the answer is x^2 - 5x + 12 and a remainder of -19 / [x + 2]
