Difference between polynomial term and degree

Question

Explain the difference between a polynomial of five terms And a polynomial with a degree of five

Answer 1

A polynomial of degree 5 is one whose highest degree is 5. For example,

f(x) = a₅x⁵ + a₄x⁴ + a₃x³ + a₂x² + a₁x + a₀

with a₅ ≠ 0. Any of the other a_i can be zero, but not a₅.

A polynomial can have 5 terms and still be of degree 5. For example,

g(x) = 2x⁵ + x⁴ + 7x³ + 14x + 11

On the other hand, a polynomial can have 5 terms and NOT be of degree 5. For example,

h(x) = 20x⁹ + 67x⁷ + 44x⁴ - 8x + 2

A polynomial of degree n can have at most n+1 terms.