5

Part of 2011 QEDMO 10th

Problems(1)

f(x) is completely reducible if f (x^{2011}) is also

Source: 10th QEDMO p5 Seniors (8-10. 12. 2011) https://artofproblemsolving.com/community/c1512515_qedmo_200507

f (x)

with real coefficients is called completely reducible if it is a product of at least two non-constant polynomials whose coefficientsare all nonnegative real numbers. Show: If

f (x^{2011})

is completely reducible, then

f(x)

polynomialalgebra