When ax^3 - 4x^2 + 5x - 3 is divided by (x +2) and (x-1), the remainders are equal. Find a.

I am unsure of this answer I worked out the remainder to be a = -3

But when I substitute it into the equation they do not match

I think you have the right answer. I divided -3x^3-4x^2+5x -3 by x+2 and also by x-1 and both times got a remainder of -5.

Here's a way to look at it if you like.

Dividing the given cubic by x-1 gives a remainder of \frac{a-2}{x-1}

Dividing by x+2 gives a remainder of \frac{-8a-29}{x+2}

a-2=-8a-29

a=-3 and -5 is indeed the remainder.

Check.