Quote:
Originally Posted by cirquedufreak
Could Someone please help me...I have no idea what to do for these two promblems
For what values of k does the function f(x) = x3 + 6x2 + kx – 4 give the same remainder when divided by (x1) and (x + 2)?
Determine the value of k when x3 + kx2 + 2x – 3 is divided by x + 2, and the remainder is 1.

1. Divide x^3 + 6x^2 + kx  4 by (x  1). This gives x^2 + 7x + (k + 7) with a remainder of k + 3. Then divide x^3 + 6x^2 + kx  4 by (x + 2).This gives x^2 + 4x + (k  8) with a remainder of 12  2k. Then set the two remainders equal to each other.
k + 3 = 12  2k
3k = 9
k = 3
2. Divide x^3 + kx^2 + 2x  3 by x + 2 giving x^2 + (k 2)x + (2  2(k  2)) with a remainder of 3  2(2  2(k 2)). Then set the remainder equal to 1 and solve for k.
3  2(2  2(k  2)) = 1
2(2  2k + 4) = 4
2  2k + 4 = 2
6  2k = 2
2k = 8
k = 4