Can anyone show me how someone came up with this answer using long division?

Question

The question was?
Using long division what is the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x) for

P(x) = x^4 +2x^3 – 2x + 4
D(x) = x - 2

This is the answer (I think).

Q(X) = X^3 + 4X^2 + 8X + 14
R(X) = 32

Answer 1

Looks good to me.
First you are dividing x4/(x-2). Then you subtract
(x^4-2x^3) from P(x) to get a reduced P(x) of
4x^3-2x+4. Dividing 4^3/(x-2), you get the 4x^2 term. Subtract (4x^3-8x^2) form the reduced P(x), you get 8x^2-2x+4. The rest follows along. The sticking point might be that there is NO x^2 term in the original equation.

Answer 2

you see how many time x-2 will go into x^4 +2x^3 – 2x + 4

so x-2 will go in to x^4, x^3 times (you always start with the leading coefficent on the bottom portion)
so that make it x^4 - 2x^3 (x-2)*(x^3)
you then subtract that from the x^4 +2x^3 – 2x + 4 and are left with 4x^3 -2x +4

x-2 goes into 4x^3, 4x^2 times
so that makes it 4x^3 - 8x^2
subtract that from what you have left of 4x^3 -2x +4. And you get 8x^2 -2x +4. This is underneath, on top you have x^3 +4x^2.

x-2 goes into 8x^2, 8x times
so that makes it 8x^2 -16x
subtract that from what you have left of 8x^2 -2x +4, and you get 14x +4

x-2 goes into 14x, 14 times
so that makes it 14x - 28
subtract that from 14x +4, and you get 32 as a remainder and you should have x^3 +4x^2+8x+14 on the top.

Hope you can understand this

Answer 3

P=x^4 + 2x^3- 2x+4
P=x^3(x+2) -2x +4
therefore P = -x^3(x-2) - 2(x-2)
by my method ... P divided by D
= -x^3-2

Answer 4

okay, well i was going to scan my work so you could see the process instead of having to read through all the steps, which you might not get as easily as just seeing the math...but you don't allow email...so, oh well...

anyway, your answer is right

Answer 5

http://www.karlscalculus.org/notes.html#plongdiv
polynomial division