



 
Hi Indrajit. Factoring cubics is not an easy thing to do generally, but you may get lucky. What I like to do is to remember that if f(x) can be factored, then there is some f(a) = 0. If I can find this value a, then I know that (xa) is a factor of f(x). Let's look at your equation: This is going to take some guesswork. So I know that (x  1/2) is a factor of 8x^{3} + 4x  3. I can use long division to find its quotient, which would have to be a quadratic. x into 8x^{3} goes 8x^{2} times. NOTE THIS. Do it again: Do it one more time: The quotient is the sum of the terms we "noted": 8x^{2} + 4x + 6. So 8x^{3} + 4x  3 = (x  1/2)(8x^{2} + 4x + 6). Now you just have to factor down the quadratic. Cheers,  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 