SOLUTION: Solve for the value/s of k so that a.) x-2 is a factor of x^3-x^2+kx-2. b.) x-4 is a factor of x^3-k^2x^2-8kx-16.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve for the value/s of k so that a.) x-2 is a factor of x^3-x^2+kx-2. b.) x-4 is a factor of x^3-k^2x^2-8kx-16.      Log On


   



Question 933067: Solve for the value/s of k so that

a.) x-2 is a factor of x^3-x^2+kx-2.
b.) x-4 is a factor of x^3-k^2x^2-8kx-16.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 
Hi
x-2 is a factor of x^3-x^2+kx-2.
2 1 -1 k -2
2 2 2k+4
1 1 k+ 2 0
k = -1 2k%2B4+=+2
.........
x-4 is a factor of x^3-k^2x^2-8kx-16
4 1 -k^2 -8k -16
4 16 - 4k^2 -16k^2 - 32k + 64
1 4-k^2 -4k^2 - 8k + 16 0
k = -3,1 -16k%5E2+-+32k+%2B+64+=+16
Synthetic Division works well here.