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Question

Factor x^2+4x+4-81x^4 into two quadratic polynomials with integer coefficients. Submit your answer in the form (ax^2+bx+c)(dx^2+ex+f), with a<d.

Accepted Answer

Note that x^2+4x+4-81x^4=(x+2)^2-(9x^2)^2=(-9x^2+x+2)(9x^2+x+2), where we have used the difference of squares identity to get the second equality.