Question

Given that the polynomial f (×)=6-×-×^2 is a factor of the polynomial g (×)=ax^3+5×^2+bx-18=0.find the values of the constants a and g.The remainder when g (x) is divided by x+2

Answer 1

If (6-x-x^2) divides g(x), then that means that (3+x) and (x-2) are both factors of g(x)

g(x)/(x+3) has a remainder of -27a-3b+27
g(x)/(x-2) has a remainder of 8a+2b+2

Since those are both zero, we have

9a+b = 9
4a+b = -1
a=2, b=-9

g(x) = 2x^3+5x^2-9x-18 = (2x+3)(x-2)(x+3)