If x + 1 is a factor of x3 + 3x2 + kx + 4, find the value of k
Answer Details
To find the value of k, we need to use the factor theorem which states that if x - a is a factor of a polynomial, then the polynomial is zero when x = a.
Since x + 1 is a factor of x^3 + 3x^2 + kx + 4, we know that x = -1 makes the polynomial zero. Substituting -1 for x in the polynomial, we get:
(-1)^3 + 3(-1)^2 + k(-1) + 4 = 0
-1 + 3 - k + 4 = 0
6 - k = 0
Solving for k, we get:
k = 6
Therefore, the value of k is 6.