Question

The polynomial of degree n has at most ________ terms. n
n-1
n+1
n+2​

Answer 1

n+1 terms.

Your highest term will be the term with power n, and after that you have the terms with n-1 power n-2 power all the way down to n-n which gives you a power of 0, (the constant term)

So total terms in an equation with n power is (n+1) terms

Hope this Helped! Have a nice day!

Answer 2

The polynomial of degree n has at most  (n + 1) terms.​

(Assumption: Polynomial with single variable)

A monomial is number, a variable, or a product of numbers and variables with whole number exponents.

A polynomial is a monomial or a sum of monomials

Degree of a Monomial

When the exponents of all variables in a monomial are summed up, the resulting number is called the degree of the monomial.

Degree of a Polynomial

Degree of a polynomial is the highest degree of its monomials.

The polynomial of degree n can have any number of terms depending upon the number of variables

For examples:

x²yz + xy²z + xyz²  + x²y² + x²z² + y²z² + xyz +  x²y + y²z + z²x + x²z + y²x + z²y   + x² + y² + z²  + xy + yz + xz + x + y + z + 1

This is a polynomial with degree 4 and has 23 terms

But any polynomial with degree n with only one variable can have maximum n+1 terms

as it can have terms with variables

xⁿ + xⁿ⁻¹ + xⁿ⁻² + ... + x² + x¹  + x⁰

If none of the coefficient of these is Zero Then

it can have n + 1 Terms

The polynomial of degree n has at most  (n + 1) terms.​

(Assumption: Polynomial with single variable)