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 $a<d$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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 $a<d$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(-4x^2+x+1)(4x^2+x+1)
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 $a<d$.
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