Question

what is degree of the polynomial x⁴(1+x⁵+x³+x²)​

Answer 1

5 is the highest power so 5 is the highest polynomial degree

Answer 2

$let \: p (x) = (x + 1) \: (x {}^{2} - x - x {}^{4} - - 1) \\ x {}^{3 \: } - x {}^{2} - x {}^{5} + x + x {}^{2} - x + x {}^{4} - 1 \\ x {}^{3} - x {}^{5} - x {}^{4} + 1 \\ the \: highest \: power \: of \: x \: is \: 5 \\ thus \: the \: degree \: of \: the \: given \: polynomial \: is \: 5$