Remainder theorem and synthetic division

Question

If (x-1) is a factor of 2x^3-kx^2+4x-1, find the value of k and use synthetic division to check . Replace the k with the answer that you get in the remainder theorem.

Answer 1

Since (x-1) is a factor, 1 is a solution to your equation.

2(1)³ - k(1)² + 4(1) -1 = 0

2 - k + 4 -1 = 0

k = 5

1 | 2 -5 4 -1

2 -3 1

2 -3 1 0

The remainder is zero, and therefore your answer for k worked out correctly!

Answer 2

Then 1 is a solution..

2-k+4-1=0

K=5