How to solve a polynomial of the form y = ax^3 + bx^2 + cx + d using the incremental algorithm in computer graphics I am studying Computer Graphics and need to design an incremental algorithm for solving the polynomial $y = ax^3 + bx^2 + cx + d$, and then implement that in OpenGL. The input will be the values of $a, b,c,d$ and the desired output is a line/curve to be drawn. The values of $x$ would be in the range $1\leq x\leq100$. The algorithm needs to be very efficient hence I am required to use only addition operation, as multiplication is less efficient.

It would be similar to this technique, but here the polynomial to be considered is the one given above. I have searched a lot on the Internet but cannot find the required solution, because most of the examples solve the equation $y = mx+b$.

Can anyone kindly guide me how to solve it or which method should be applied to solve it?
You have f(x). Let g(x) = f(x+1) - f(x). Let h(x) = g(x+1) - g(x). Let k(x) = h(x+1) - h(x). It turns out that k(x) is a constant. 

Calculate f(x), g(x), h(x) and k(x) for x = 1. Then you calculate f(x+1) = f(x) + g(x), g(x+1) = g(x) + h(x), h(x+1) = h(x) + k(x), and k(x) is a constant.