SOLUTION: Find "k" so when x^3 + kx^2 - kx + 1 is divided by x-2, the remainder is 0.

Question 265252: Find "k" so when x^3 + kx^2 - kx + 1 is divided by x-2, the remainder is 0.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
One way to solve is via synthetic division. First we divide by x-2. Set this equal to zero and solve for x to get x = 2.
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2 // . . . . 1 . . . . k . . . .-k . . . . . 1
. . . . . . . . . . . . .2 . . . . 2k+4 . . . 2k+8
. . . . . . . 1 . . . . k+2 . . .k+4 . . . .2k+9
2k+9 = 0
2k = -9
k = -9/2
So, the polynomial is
x^3 + (-9/2)x^2 + (9/2)x + 1
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