You are here:

Algebra/Algebra 2 3rd Degree Polynomial Factoring Question


Our teacher provided us a review packet for a test tomorrow.  There is one equation/question that has me stumped.  

I am given the equation f(x)= x^3-x^2-12, and asked to find the zeros for this.  Now, I first looked at substituting a variable (say t) for x^2, but that won't work because it is of degree 3.

Next, I tried adding variables then regrouping, to see if I could factor out a root, but that does not work either.  It would work if the equation was x^3+x^2-12, but alas it is not.

I even tried using my calculator once I found the factors of p and q (rational root theorem), but that got me nowhere.

I believe the answer is that you cannot find the roots using simple methods, but my teacher seems to feel you can.  

Can you provide any help?

For the equation provided, it has one real root with value 2.676 (correct to 3 dp) and two complex conjugate roots.

In such an instance, your methods suggested will not be feasible. Even the rather light-touch approach of the factor theorem will not work.

One plausible way to solve this would be via the Newton-Raphson method, though I am unsure if you have been taught such a technique. It involves a preliminary educated guess for the value of one of the roots, and it definitely isn't a "simple" method.

My advice? Don't worry too much about this question.



All Answers

Answers by Expert:

Ask Experts


Frederick Koh


I can answer questions concerning calculus, complex numbers, vectors, statistics , algebra and trigonometry for the O level, A level and 1st/2nd year college math/engineering student.


More than 7 years of experience helping out in various homework forums. Latest presence is over at You can also visit my main maths website where I have designed "question locker" vaults to store tons of fully worked math problems. A second one is currently being built. Peace.

IEEE(Institute of Electrical and Electronics Engineers )

Former straight As A level student from HCJC (aka HCI); scored distinctions in both C and Further Mathematics B Eng (Hons) From The National University Of Singapore (NUS) B Sc (Hons) From University of London External (Grad Route)

©2016 All rights reserved.