SOLUTION: the polynomial function f(x)=x^3+x^2-5x-6 has a zero at x=-2.that implies that x+2 must be a factor of the polynomial. find the other factors by either polynomial long division, or

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: the polynomial function f(x)=x^3+x^2-5x-6 has a zero at x=-2.that implies that x+2 must be a factor of the polynomial. find the other factors by either polynomial long division, or      Log On


   

Question 38023: the polynomial function f(x)=x^3+x^2-5x-6 has a zero at x=-2.that implies that x+2 must be a factor of the polynomial. find the other factors by either polynomial long division, or synthetic division...i really dont mind which process you choose, i just need help grasping these concepts. id say im more familiar with polynomial long division. this is part of a take home extra credit assignment i was given, so i dont have any book info, thank you so much!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=x^3+x^2-5x-6 has a zero at x=-2
Use your long division.
Divide f(x) by x+2 and you will get a
quotient of x^2-x-3 and with a remainder
of zero.
Now solve the quotient for x by using the
quadratic formula, as follows:
x=[1+sqrt(1+12)]/2=[1+-sqrt(13)]/2
This means the other two factors are:
(x-[(1/2)+(1/2)sqrt13]) and (x-[(1/2)-(1/2)sqrt13])
Cheers,
Stan H.