This resource is from Underground Mathematics (previously known as the Cambridge Mathematics Education Project).
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 funded by a grant from the UK Department for Education and provides free web-based resources that support the teaching and learning of post-16 mathematics. It started in 2012 as the Cambridge Mathematics Education Project (CMEP).
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.