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I have re-labelled your image for convenience. In future, please refer to documentation re: posting code rather than images. I may have made some transcription errors but perhaps this will point you in direction you are aiming for. e1 = a x^2 + c y^2 + b x y e2 = 2 c y z + 2 a w x + 2 b (x z + y w) e3 = a w^2 + c z^2 + b w z Factor[PolynomialMod[Expand[e2^2 ...


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This is not as versatile as Chip's method but it might be sufficient: rule = {x_^a_ + y_^b_ /; Divisible[a, b] :> (x^(a/b) + y)^b}; {q^3 + r^3, f[x]^2 + f[y]^4} /. rule {(q + r)^3, (f[x] + f[y]^2)^2}


3

I think we can just use basic pattern matching: (* Freshman's dream... ahhhhh *) FrobeniusFactor[expr_] := expr //. x_^e1_ + y_^e2_ :> With[{g = PolynomialGCD[e1, e2]}, ( (x^Cancel[e1/g] + y^Cancel[e2/g])^g ) /; g =!= 1 ] FrobeniusFactor[x^a + y^a] (x + y)^a FrobeniusFactor[f[x]^2 + f[y]^4] (f[x] + f[y]^2)^2


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expr = 2 x^2 + 7 x + 2; expr2 = (x + a) (x + b) + x (x + c); expr2 /. Solve[Equal @@ (CoefficientList[#, x] & /@ {expr, expr2}), {a, b, c}, Integers][[-1]] (1 + x) (2 + x) + x (4 + x)



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