This resource is from Underground Mathematics.
Can you design a polynomial in $x$, $p(x)$, such that $p(x)=p'(x)$?
(a) What is the simplest polynomial in $x$ you can think of and what is its derivative?
(b) What powers of $x$ do you want the polynomial to include and what does this mean for the derivative?
This is an Underground Mathematics resource.
Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.
Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.