Q2) n ਘਾਤੀ ਬਹੁਪਦ ਵਿੱਚ ਪਦਾਂ ਦੀ ਗਿਣਤੀ ਵੱਧ ਤੋਂ ਵੱਧ ______ ਹੁੰਦੀ ਹੈ। The polynomial of degree n has at most ________ terms. *
Answers
Answer:
the answer is n+1
Step-by-step explanation:
the ans is n+1
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)