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Thanks for the report. Looks like a terrible bug! It was introduced in SageMath 8.4: it is already there, while in SageMath 8.3, we get a mathematically correct result:

sage: factor(exp(-x)+2*exp(x))
(2*e^(2*x) + 1)*e^(-x)

Thanks for the report. Looks like a terrible bug! It was introduced in SageMath 8.4: it is already there, while in SageMath 8.3, we get a mathematically correct result:

sage: factor(exp(-x)+2*exp(x))
(2*e^(2*x) + 1)*e^(-x)

I've opened the Trac ticket #27304 for it.