determine the value k in f(x) such that x + 1 is a factor of f(x).\n$f(x)=x^{3}+3x^{2}+kx - 4$\nthe value of…

determine the value k in f(x) such that x + 1 is a factor of f(x).\n$f(x)=x^{3}+3x^{2}+kx - 4$\nthe value of k is something else.\nk = 2\nk = 4\nk = - 2

determine the value k in f(x) such that x + 1 is a factor of f(x).\n$f(x)=x^{3}+3x^{2}+kx - 4$\nthe value of k is something else.\nk = 2\nk = 4\nk = - 2

Answer

Explanation:

Step1: Apply factor - theorem

If (x + 1) is a factor of (f(x)=x^{3}+3x^{2}+kx - 4), then (f(-1)=0) according to the factor - theorem.

Step2: Substitute (x=-1) into (f(x))

[ \begin{align*} f(-1)&=(-1)^{3}+3(-1)^{2}+k(-1)-4\ &=-1 + 3-k - 4 \end{align*} ]

Step3: Set (f(-1) = 0) and solve for (k)

[ \begin{align*} -1+3 - k-4&=0\ -2-k&=0\ k&=-2 \end{align*} ]

Answer:

(k=-2)