SOLUTION: how do i divide x^4-2x+1 by x-2

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Question 451734: how do i divide x^4-2x+1 by x-2
Found 2 solutions by stanbon, pedjajov:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
how do i divide x^4-2x+1 by x-2
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Using synthetic division:
2)....1....0....0....-2....1
.......1....2....4....6....|13
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Quotient: x^3+2x^2+4x+6
Remainder: 13
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Cheers,
Stan H.
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Answer by pedjajov(51) About Me  (Show Source):
You can put this solution on YOUR website!
You divide one polynomial with the other one by dividing highest terms.
But first we have to write polynomials like they have terms with all exponents,

x%5E4-2x%2B1+=+x%5E4%2B0x%5E3%2B0x%5E2-2x%2B1

For example for these two at the beginning highest terms are x^4 in first and x in the second. Dividing these two gives us x^3.
Now we should multiply x^3 with (x-3).
We get x^4-2x^3. We subtract like terms to get 2x^3.
Now we drop down next term 0x^2 and we repeat previous until we get to the terms we can't make division anymore. What's left is a reminder

Here is how it looks for this problem:

x^4+0x^3+0x^2-2x+1 / x-2 = x^3+2x^2+4x+6
x^4-2x^3
--------
2x^3+0x^2
2x^3-4x^2
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4x^2-2x
4x^2-8x
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6x+1
6x-12
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+13

Check:
%28x-2%29%28x%5E3%2B2x%5E2%2B4x%2B6%29+%2B13
x%5E4%2B2x%5E3%2B4x%5E2%2B10x-2x%5E3-4x%5E2-8x-12%2B13
x%5E4-2x%2B1