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

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) (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.
RELATED QUESTIONS
Give that the polynomial function has the given zero, find the other zeros. f(x)=... (answered by Edwin McCravy)

Given that the polynomial function has the given zero, find the other zeros. f(x)=... (answered by stanbon)

Find a fifth-degree polynomial that has a zero of multiplicity 2 at x = 2, a zero at x =... (answered by swincher4391)

find a fifth degree polynomial that has a zero of multiplicity 2 at x=2, a zero at x=5,... (answered by solver91311)

Use the intermediate value theorem to show that the polynomial function has a zero given... (answered by fcabanski)

-2;p(x)=3x^3+5x-6 is -2 a zero of the polynomial(x)... (answered by josgarithmetic)

find a rational zero of the polynomial function and use it to find all the zeros of the... (answered by stanbon)

show that the polynomial f(x)=x^4 4x^2 6 has no... (answered by Alan3354)

Factor each polynomial completely given that the binomial following it is a factor of the (answered by tutorcecilia)