Question

For what value of c is p(x) = 2x^4 - 5x^2 + cx - 1 divisible by x - 1? Show work.

Answer 1

c = 4

Explanation:

if (x - a) is a factor , that is divisible by, of f(x) then f(a) = 0

then for p(x) to be divisible by (x - 1) , p(1) = 0

then

2
`(1)^(4)` - 5(1)² + c(1) - 1 = 0

2 - 5 + c - 1 = 0

- 4 + c = 0 ( add 4 to both sides )

c = 4