need help with a division problem?

Question

(x^4 + x^3 - 3x - 3) divided by (x + 1)

Answer 1

(x^4 + x^3 - 3x - 3) =
x^3(x+1)-3(x+1) =
(x+1)(x^3-3)
therefore the result is x^3-3

Answer 2

There are 2 ways to do this...
A. Long Division
B. Symplification

The easiest would be simplification.
Set up your problem like this:
x^4+x^3-3x-3
x+1 as if it were a fraction. Like with a line underneath the quartic polynomial. Then factor the quartic by grouping which looks like this:
(x^4+x^3)-(3x-3)
x cubed factors out of the first group and negative 3 factors out of the second
x^3(x+1)-3(x+1)
Put the outside factors together and make the insides count as one and you are left with:
(x^3-3)(x+1)
Then you have that ^ on the top and x+1 on the bottom. The two x+1 quantities cancel out and you are left with x^3-3.
If you did long division you would get the same thing. :-)

Answer 3

(x^4 + x^3 - 3x - 3) divided by (x + 1)
= (x^3 -3)

Answer 4

x^3-3

Answer 5

x^3-3

Answer 6

This can be solved three different ways:
1. long division
2. synthetic division
3. factoring by grouping in the denominator then reducing the fraction

I think choice #3 is the easiest!

grouping: (x^4+x^3)+(-3x-3)/(x+1)
factoring: x^3(x+1)-3(x+1)/(x+1)
factoring: (x+1)(x^3-3)/(x+1)
reduce: x^3-3

Answer 7

(x^4 +x^3 -3x -3) / (x +1)
[x^3(x +1)] /(x+1) -[3(x +1)] /(x +1)
... now the (x+1) terms cancel out
x^3 -3

ANS: x cubed minus 3