Question 1058807: Use the factor theorem to prove that x^2 - x - 2 is a factor of x^3 - 6x^2 +3x + 10 Found 2 solutions by Boreal, stanbon:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! One can use synthetic division on each of the factors that make up x^2-x-2, (x-2)(x+1)
2/1===-6---3---10
--1===-4==-5==0
-1/1===-6==3==10
==1===-7==10==0
one can use long division, too.
========x-5
x^2-x-2/x^3-6x^2+3x+10
======x^3-x^2-2x
========-5x^2+5x+10
========-5x^2+5x+10
change signs and remainder is 0
The third factor is (x-5).
You can put this solution on YOUR website! Use the factor theorem to prove that
x^2 - x - 2 is a factor of x^3 - 6x^2 +3x + 10
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Divide the cubic by the quadratic to get (x-5)
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Cheers,
Stan H.
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