The polynomial of degree n has at most ________ terms.​

  • matematika

    Subject:

    Math
  • Author:

    cheeky
  • Created:

    1 year ago

Answers 2

Answer:

n+1

Step-by-step explanation:

Numbers of terms in the polynomial of degree n=1is 2. The Number of terms in the polynomial of degree n=2is 3. Therefore, the number of terms in the polynomial of degree nis n+1.

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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)

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