Question

What is the correct answer?

Answer 1

The value of k is -4. Third choice

Step-by-step explanation:

The Polynomial Remainder Theorem

It states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).

We are given the polynomial:

`p(x)= x^3+kx^2+x+6`

And we also know x+1 is a factor of p(x). If x+1 is a factor of p(x), then the remainder of the division of p(x) by x+1 is zero.

Applying the remainder theorem for a = -1:

`p(-1)= (-1)^3+k(-1)^2+(-1)+6=0`
`-1 + k - 1 + 6 = 0`

Solving for k:

`k = 1 + 1 - 6`

`\boxed{k = -4}`

The value of k is -4. Third choice