Algebra · Polynomial divisibility · Factor theorem · Repeated roots
Find every real value of the parameter \(a\) for which the polynomial
\[ P(x) = x^{2021} - 2x^{2} + x + a^{3} - a \]
is divisible by the polynomial
\[ Q(x) = x^{2} - (a+1)x + a. \]
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Regional Competition (Okruzno takmicenje) 2021, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source