Question 36042
5x^3 + 9x^2 + 18x - 4
= 5x^3 - x^2 + 10x^2 - 2x + 20x - 4
= x^2(5x-1) + 2x(5x-1) + 4(5x-1)
= (5x-1)(x^2 + 2x + 4)...(1)
When (1) is divided with (5x-1), the result is (x^2 + 2x + 4)
Answer: (x^2 + 2x + 4)
I used a long division approach mentally to determine how I should break the expression in a way so that I can factor them properly.
You may want to use the long division approach, or synthetic division approach to do this kind of division.  Please note that the synthetic division works only when you are to divide by a linear expression.  There will be instances when you will find a remainder when dividing with a ceratin expression.