SOLUTION: I need your help to solve the following: Divide: (4x^4 - 12x^3 - 48x - 60) + (x - 4) This question is from a worksheet.

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Question 119638: I need your help to solve the following:
Divide: (4x^4 - 12x^3 - 48x - 60) + (x - 4)
This question is from a worksheet.
Found 2 solutions by tangitehewagen, benbjlin:
Answer by tangitehewagen(7) About Me  (Show Source):
You can put this solution on YOUR website!
I am assuming you mean
Divide: %284x%5E4+-+12x%5E3+-+48x+-+60%29 by %28x+-+4%29
If so, then we start by asking what quantity multiplied by x results in 4x%5E4 which we can see is 4x%5E3. We then multiply -4 by 4x%5E3 to get -16x%5E3 and subtract from -12x%5E3 which gives us 4x%5E3.
So now we want to know what 4x%5E3+%2B+0+x%5E2+-+48x+-+60 divided by x+-+4 is. We start as in the first step and ask what quantity multiplied by x gives us 4x%5E3. The answer to this question is 4x%5E2. Multiplying -4 by 4x%5E2 results in -16x%5E2. Subtracting -16x%5E2 from 0x%5E2 leaves us with 16x%5E2.
The next division is 16x%5E2+-+48x+-+60 by x+-+4. As we have done previously, we ask what we need to multiply x by to get 16x%5E2 and find that the quantity would be 16x. Multiplying 16x by -4 gives us -64x and subtracting from -48x gives us 16x.
Finally, we want to know what 16x+-+60 divided by x+-+4 is. We see that 16x divided by x is 16 and multiplying -4 by 16 results in -64. Subtracting -64 from -60 gives us a remainder of 4.
Thus %284x%5E4+-+12x%5E3+-+48x+-+60%29 divided by %28x+-+4%29+=+4x%5E3%2B4x%5E2%2B16x%2B16+%2B+4%2F%28x-4%29.

Answer by benbjlin(6) About Me  (Show Source):
You can put this solution on YOUR website!
I assume you mean:
(4x^4 - 12x^3 - 48x - 60) / (x - 4)
The most straight forward way is to solve this long division style. We will use 0x^2 as a place holder. As follows:

:::::::::::::::::4*x^3 + 4*x^2 + 16*x + 16 + 4/(x-4)
_____________________________________
(x-4) | 4*x^4 - 12*x^3 - 0*x^2 - 48*x - 60
::::::-(4*x^4 - 16*x^3)
::::::________________
:::::::::::0 4*x^3 - 0*x^2
:::::::::::::::-(4*x^3 - 16*x^2)
:::::::::::::::________________
:::::::::::::::::::0 16*x^2 - 48*x
:::::::::::::::::::::::-(16*x^2 - 64*x)
:::::::::::::::::::::::_______________
:::::::::::::::::::::::::::0 16*x - 60
::::::::::::::::::::::::::::::::-(16*x - 64)
::::::::::::::::::::::::::::::::___________
::::::::::::::::::::::::::::::::::::::::::4
Factor 4 out from: 4x^3 + 4x^2 + 16x + 16 + 4/(x-4)
4*(x^3 + x^2 + 4x + 4 + 1/(x-4))
Check:
1. (x-4)*4*(x^3 + x^2 + 4*x + 4 + 1/(x-4)) Multiply 4 into (x^3...)
2. (x-4) * (4*x^3 + 4*x^2 + 16*x + 16 + 4/(x-4)) Multiply (x-4) into (4*x^3...)
3. 4*x^4 - 16*x^3 + 4x^3 - 16*x^2 + 16*x^2 - 64*x + 16*x - 64 + 4 Simplify
4. 4*x^4 - 12*x^3 - 48*x - 60