SOLUTION: Given a polynomial and one of it's factors,find the remaining factors of the polynomial.Some factors may not be binomials. solve for three x cubed plus ten x squared minus x minus

Algebra ->  Rational-functions -> SOLUTION: Given a polynomial and one of it's factors,find the remaining factors of the polynomial.Some factors may not be binomials. solve for three x cubed plus ten x squared minus x minus      Log On


   



Question 24707: Given a polynomial and one of it's factors,find the remaining factors of the polynomial.Some factors may not be binomials.
solve for three x cubed plus ten x squared minus x minus twelve divided by x plus three.

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
solve for three x cubed plus ten x squared minus x minus twelve divided by x plus three.
N.R.=F(X)=3X^3+10X^2-X-12...WE FIND THAT WHEN X=1 ,F(X)=0..HENCE X-1=0..SO DIVIDING BY X-1 USING SHORT DIVISION ...
1...|...3..........10...........-1..............-12
....|...0...........3...........13...............12
---------------------------------------------------------
....|...3..........13...........12................0
SO THE QUOTIENT IS 3X^2+13X+13..NO FURTHER RATIONAL FACTORS ARE POSSIBLE.SINCE B^2-4AC=13^2-4*3*13=169-156=13 IS NOT A PERFECT SQUARE.
SO N.R./D.R.=(X-1)*(3X^2+13X+13)/(X+3)