# Playing with Polynomials

We’ll be doing a little bit of review work in the Integrated CME Project III book. Today my son came across an interesting problem about trying to (sort of) match two polynomials. He came up with a nice solution this morning and we talked about the problem when he got home from school today.

The problem goes like this:

Find a polynomial that agrees with $x^3 - x$ at $x = 1, 2$, and 3, and has a value of 0 at x = 4.

Here’s my son talking through his solution:

After he finished his explanation, I showed him my solution to the problem:

To wrap up we went to Mathematical to look at both solutions and also so that I could show him a little surprise:

So, a nice start to this review project. It’ll be fun to work through the book over the summer.