Question

find k such that f(x)=2x^3+kx^2-7x+6 has a factor of x+2 (can someone help me work this out)
not just the answer

Answer 1

I would use synthetic division to solve this problem, example can be found here http://en.wikipedia.org/wiki/Synthetic_division

The result should look something like this
2 k -7 6
-2 -4 8-2k 4k-2
-------------------------
2 k-4 1-2k 4k+4

the terms 2, k-4, 1-2k are the coefficients of the second order polynomial once you divide out the x+2. The term 4k+4 is the remainder from the division. Since we want a remainder of 0, take k=-1.

From there, you have k-4 = -5 and 1-2k = 3, and your divided out polynomial is x^2-5x+3. To check, multiply out (x+2)(x^2-5x+3) and you should see the same polynomial that you started with.