Answer:
The value of k is -4. Third choice
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:
[tex]p(x)= x^3+kx^2+x+6[/tex]
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:
[tex]p(-1)= (-1)^3+k(-1)^2+(-1)+6=0[/tex][tex]-1 + k - 1 + 6 = 0[/tex]
Solving for k:
[tex]k = 1 + 1 - 6[/tex]
[tex]\boxed{k = -4}[/tex]
The value of k is -4. Third choice
