Answer:
(x + 3) a factor of the polynomial p(x) = k * x^3 + x^2 + 22x - 24 is -3.
Step-by-step explanation:
To determine the value of k such that (x + 3) is a factor of the polynomial p(x), we can use the factor theorem.
According to the factor theorem, if (x + 3) is a factor of p(x), then p(-3) must equal zero.
Let's substitute -3 for x in the polynomial p(x) and set it equal to zero:
k * (-3)^3 + (-3)^2 + 22 * (-3) - 24 = 0
Simplifying the equation:
k * (-27) + 9 - 66 - 24 = 0
-27k - 81 = 0
To isolate k, let's move -81 to the other side of the equation:
-27k = 81
Now, divide both sides of the equation by -27:
k = 81 / -27
Simplifying the expression:
k = -3
Therefore, the value of k that makes (x + 3) a factor of the polynomial p(x) = k * x^3 + x^2 + 22x - 24 is -3.
