IB231997 Posted August 28, 2012 Report Share Posted August 28, 2012 x3 – 19x + 30how do you factorize this polynomial ? Reply Link to post Share on other sites More sharing options...
Fermat Posted August 28, 2012 Report Share Posted August 28, 2012 You can use the rational root test [ find a factor on the form (px-q) where p is a factor of 1 and q is a factor of 30] or if you are allowed to use a calculator, plot the function and find a root (a factor) then you can use synthetic division to find the other factors. 1 Reply Link to post Share on other sites More sharing options...
macrofire Posted August 29, 2012 Report Share Posted August 29, 2012 write it out in the form (x-a)(x^2+bx+c) equation (1)expand to get x^3 + (b-a)x^2+(c-ab)x-acequate it to your equation. find equivalences for the coefficientsNow let's assume that the coefficients are integersNote that ac = -30, b-a=0 and c-ab=-19This implies that a=b => c-a^2=-19Find the numbers that fit those two equations ac=-30 and c-a^2=-19Plug back into (1) and factor the quadraticThis method doesn't always work. There is a general formula, but it's too complicated. It's better to assume that there's integer answers and try from there than to be stuck and stare at the paper for hours. 2 Reply Link to post Share on other sites More sharing options...
Aura Posted November 9, 2012 Report Share Posted November 9, 2012 How about Ruffini's rule? (Sorry for the old-thread bump) Reply Link to post Share on other sites More sharing options...
macrofire Posted November 11, 2012 Report Share Posted November 11, 2012 ruffini's rule works well with integers. It gets messy if you put in enough grime. Reply Link to post Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.