problem: Factor $-16x^4+x^2+2x+1$ into two quadratic polynomials with integer coefficients.  Submit your answer in the form $(ax^2+bx+c)(dx^2+ex+f)$, with $a<d$.
solution: Note that $-16x^4+x^2+2x+1=(x+1)^2-(4x^2)^2=\boxed{(-4x^2+x+1)(4x^2+x+1)}$, where we have used the difference of squares identity for the second equality.