Using the factors (-1) and (x-4) find the remaining factor(s) of f(x) = x^3 - 2x^2 - 11x + 12 and write the polynomial as a product of linear factors

Question

mathmale · Answer

One way to approach this problem would be to divide the given polynomial, f(x), by x-1 and x-4 (separately).  Doing this will leave you with the one remaining factor.  We know that there are 3 factors because the order of the poly. is 3.

I'd suggest using synth. div. if you know it.

Try     4  |  1   -2    -11   12

               ---------------
                  1

mathmale · Answer

Otherwise, try dividing (x-4) into x^3 -2x^2 - 11x +12.

anonymous · Answer

I come up with (x*3) as my other factor so the product if linear factors would be. (-1)(x+3)(x-4)

whpalmer4 · Answer

are you sure it isn't supposed to be $(x-1)$ as a factor, not just $-1$?

anonymous · Answer

Yes it is (x-1)

mathmale · Answer

Then it appears that you have completely answered this question.  Your polynomial can now be written as f(x) = x^3 - 2x^2 - 11x + 12 = (x-1)(x+3)(x-4).  Nice work!