The given polynomial is
30x^3 + 83x^2 + 37x - 30
We want to divide it by 3x + 5. We would apply the method of long division. The steps are shown below
The result of dividing 30x^3 + 83x^2 + 37x - 30 by 3x + 5 = 10x^2 + 11x - 6
This is a quadratic polynomial. We would simplify this quadratic polynomial by applying the method of factorisation. The first step is to multiply 10x^2 with - 6. It becomes - 60x^2. We would find two terms such that their sum or difference is 11x and their product is - 60x^2. The terms are 15x and - 4x. By replacing 11x with 15x - 4x, we have
10x^2 + 15x - 4x - 6
We would factorise by grouping. We have
5x(2x + 3) - 2(2x + 3)
Since 2x + 3 is common, it becomes
(2x + 3)(5x - 2)
The other two factors are (2x + 3)(5x - 2)