Find a cubic polynomial such that

Since is a cubic polynomial we write,

Then,

Finally, from the integral equation we have,

Now, we have the following three equations in three unknowns,

Since we don’t know any linear algebra, we’ll use elimination to solve for each variable. (If you know some linear algebra, you might know quicker ways to solve this system of equations.) First, adding the first and second equations we obtain

Substituting this value of into the first equation we have

Finally, substituting our values of and into the last equation and solving for we get

And thus, using the equations we already have for and , we get,

Hence,