Question 207322: Finding the quotient and remainder of (w^3+1)/(w+1)
I need help figuring this problem out. I am not sure If I did it write. I just need to make sure our answers match.
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! w^3 + 1,,,pls recognize this as a cube form,,a^3 +b^3, which factors to :
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(a+b)*(a^2 -ab +b^2),,,,,now with a=w,,,,and b=1,,,we find
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(w+1) * (w^2 -w + 1)
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The problem probably wants us to use polynomial division, so let's try that.
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Remember to "fill" all the terms
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,,,,,,,,,,,,,,,,w^2,,-w,,,+1
,,,,,,,,,,____________________________________
(w+1),,,,[ w^3 +0 w^2 +0w +1
.,,,,,,,,,,w^3 +w^2
.,,,,,,,,,_________
.,,,,,,,,,,,,,,-w^2 + 0w
,,,,,,,,,,,,,,,-w^2 -w
,,,,,,,,,,,,,,,__________
,,,,,,,,,,,,,,,,,,,,,+w +1
,,,,,,,,,,,,,,,,,,,,,+w +1
,,,,,,,,,,,,,,,,,,,,,,______
,,,,,,,,,,,,,,,,,,,,,,,,,,0...........NOTE REMAINDER = 0
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as this matches factoring form, this is correct answer
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