SOLUTION: How can i use the rational root theorem and polynomail long division to factor the following completely? x^3+3x^2+3x+1

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Question 320799: How can i use the rational root theorem and polynomail long division to factor the following completely? x^3+3x^2+3x+1
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
From the rational roots theorem,
p=0+%2B-+1
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x=1
f%281%29=1%2B3%2B3%2B1=8
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x=-1
f%28-1%29=-1%2B3-3%2B1=0
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So x=-1 is a root and x%2B1 is a factor of the polynomial.
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Now use polynomial long division to find the remaining quadratic,
First term: highlight%28+x%5E2%29
x%5E2%28x%2B1%29=x%5E3%2Bx%5E2
Subtract that product from the original polynomial to get the remainder,
%28x%5E3%2B3x%5E2%2B3x%2B1%29-%28x%5E3%2Bx%5E2%29=2x%5E2%2B3x%2B1
Second term:highlight%282x%29
2x%28x%2B1%29=2x%5E2%2B2x
Subtract that product from the previous remainder to get the new remainder,
%282x%5E2%2B3x%2B1%29-%282x%5E2%2B2x%29=x%2B1
Final term:highlight%281%29
1%28x%2B1%29=x%2B1
Subtract that product from the previous remainder to get the new remainder,
%28x%2B1%29-%28x%2B1%29=0
Gather all of the terms.
%28x%5E3%2B3x%5E2%2B3x%2B1%29%2F%28x%2B1%29=x%5E2%2B2x%2B1=%28x%2B1%29%5E2
x%5E3%2B3x%5E2%2B3x%2B1=%28x%2B1%29%5E3
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A triple root at x=-1