Question

multiple choice 1 point

1. find the value of k so that the remainder of ((x^3 - 3x^2 + kx - 6) div (x + 2)) is 0.

a. 11
b. 6
c. -13
d. -11

Explanation:

Step1: Apply Remainder Theorem

Set $x + 2 = 0$, so $x = -2$. Substitute $x=-2$ into the polynomial, set result to 0:
$$(-2)^3 - 3(-2)^2 + k(-2) - 6 = 0$$

Step2: Simplify the left-hand side

Calculate each term:
$$-8 - 3(4) - 2k - 6 = 0$$
$$-8 - 12 - 6 - 2k = 0$$
$$-26 - 2k = 0$$

Step3: Solve for k

Isolate the term with k, then solve:
$$-2k = 26$$
$$k = \frac{26}{-2} = -13$$

Answer:

C. -13