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Omni-MATH / For each integer m, consider the polynomial P_(m)(x)=x⁴−(2m+4)x²+(m−2)². For what values of m is P_(m)(x) the product of two non-constant polynomials with integer coefficients?

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problem

For each integer mm, consider the polynomial Pm(x)=x4−(2m+4)x2+(m−2)2.P_m(x)=x^4-(2m+4)x^2+(m-2)^2. For what values of mm is Pm(x)P_m(x) the product of two non-constant polynomials with integer coefficients?
Plain-text mathematical notation (without MathML)
For each integer m, consider the polynomial P_(m)(x)=x⁴−(2m+4)x²+(m−2)². For what values of m is P_(m)(x) the product of two non-constant polynomials with integer coefficients?
Original LaTeX notation
For each integer $m$, consider the polynomial \[P_m(x)=x^4-(2m+4)x^2+(m-2)^2.\] For what values of $m$ is $P_m(x)$ the product of two non-constant polynomials with integer coefficients?

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Source and history

task_id
b941be4c-9575-5284-84f8-be7aaf336430
task_key
test--b941be4c-9575-5284-84f8-be7aaf336430
task_revision_id
1
config / split
/ test

Official source

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