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Question 1053225: Use polynomial division to find the quotient Q(x) and the remainder R(x) when the first polynomial is divided by the second polynomial.
1. X^4-x^3+2x^2-x+1, x^2+1
2. X^5+32,x-2
3. 6x^4-x^2+4, x-3
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x^4-x^3+2x^2-x+1 by x^2+1
=======x^2+x+1
x^2+1/x^4+x^3+2x^2-x+1
======x^4+=====x^2
subtract===x^3+x^2-x+1
===========x^3+====-x
subtract=======x^2-2x+1
===============x^2+1
subtract, and remainder -2x. Q(x)=x^2+x+1, R(x)=-2x
=
x^5+32 by x-2-------------------------------------
=====x^4+2x^3+4x^2+8x+16
x-2/x^5+0x^4+0x^3+0x^2+0x+32
====x^5-2x4
subtract 2x^4+============32
=========2x^4-4x^3
subtract======-4x^3========32
===============4x^3-8x^2
subtract=============8x^2+32
=====================8x^2-16x
subtract===================+16x+32
===========================-16x+32
subtract====================0 Q(x)=x^4+2x^3+4x^2+8x+16, R(x)=0
------------------------------------------
======6x^3+18x^2+53x+159
x-3/6x^4+0x^3-x^2+0x+4
====6x^4-18x^3
subtract 18x^3-x^2+4
========18x^3-54x^2
subtract======53x^2+0x+4
==============53x^2-159x
subtract===========159x+4
===================159x-477
subtract================+481 Q(x)=6x^3+18x^2+53x+159. R(x)=481
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