Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. If (x + 2) is a factor of x3 − 6x2 + kx + 10, k = .

Answer 1

If x+2 is a factor of x^3+6x^2+kx+10, then if we replace x by -2 in the polynomial x^3-6x^2+kx+10, we must get zero:
x=-2→(-2)^3-6(-2)^2+k(-2)+10=0→
-8-6(4)-2k+10=0→
-8-24-2k+10=0
-2k-22=0
Solving for k. Adding 22 both sides of the equation:
-2k-22+22=0+22
-2k=22
Dividing both sides of the equation by -2:
-2k/(-2)=22/(-2)
k=-11

Answer: k = - 11