Question

Given f(x) = x^3 + kx + 2, and x + 1 is a factor of f(x), then what is the value of
k?

Answer 1

k = 1

Explanation:

Given that,

`f(x) = x^3 +kx + 2`

If (x+1) is a factor of (x), we need to find the value of k.

Using remainder theorem to find it.

Put (x+1) = 0

x = -1

Put x = -1 in equation below.

`x^3 + kx + 2=0\\\\(-1)^3+k(-1)+2=0\\\\-1-k+2=0\\\\1-k=0\\\\k=1`

So, the value of k is 1.