How to factor 3rd degree polynomial with 3 terms

  • #1
575
47
-x^3+12x+16

Every single technique I read about online of how to factor 3rd degree polynomials, it says to group them. I don't think grouping works with this. I tried but it didn't work, since there's only 3 terms. Apparently I'm not supposed to have a cubic variable without a squared variable? I don't know. But how is this done?

Thanks.
 

Answers and Replies

  • #3
dextercioby
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By <eyesight> , +4 is a root of the polynomial.
 
  • #4
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The rational root theorem is a good place to start. For your problem, the only possible candidates for rational roots are ±1, ±2, ±4, ±8, or ±16. You can check each one very quickly by using synthetic division, or a bit more laboriously by using ordinary polynomial division.

Once you find one root of a cubic, the other factor is a quadratic, so you can use the quadratic formula to find the other roots.
 
  • #5
575
47
Thanks for the responses. This was part of my linear algebra homework, and the teacher's answers just shows it factored, as if it's a simple factoring procedure that everyone should know how to do. The only examples gone over in class were the typical quadratic factoring. Math teachers are usually pretty dirty, so it's not surprising she would throw in a cubic and expect us to remember how to do synthetic division or whatever.

Thanks.
 

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