Monomial, binomial, trinomial, multinomial, polynomial of Algebra Glossary

Monomial in Algebra :

An algebraic expression containing only one term is called a monomial.

Examples: Each one of 3x, -7y, 5xy, 4, -8, 6ab^{2}c, 2a⁄b^{2} is a monomial.

Binomial in Algebra :

An algebraic expression containing two unlike terms is called a binomial.

If the two terms are like terms, we can combine them and make it as one.

Examples:

(i) 9x + 10 is a binomial having two terms 9x and 10.

(ii) -3ab^{2} + 9b^{2}a is NOT a binomial. Because the two terms are like terms. You can see -3ab^{2} + 9b^{2}a = -3ab^{2} + 9ab^{2} = 6ab^{2} is a single term.

(iii) 9x - 5⁄y is a binomial having two terms 9x and - 5⁄y.

(iv) a^{2}b + 9ab^{2}c is a binomialhaving two terms namely a^{2}b and 9ab^{2}c.

Trinomial in Algebra Glossary :

An algebraic expression containing three unlike terms is called a trinomial.

Examples:

(i) 2x + 3y + 4 is a trinomial having three terms 2x, 3y and 4.

(ii) 7xy + 5yz + 6zx is a trinomial having three terms 7xy , 5yz and 6zx .

(iii) 4x^{2} - 5y⁄2 + 3z^{2} is a trinomial having three terms 4x^{2}, -5y⁄2 and 3z^{2}.

(iv) 2a + 3⁄b -4⁄c^{2} is a trinomial having three terms 2a, 3⁄ b and - 4⁄c^{2}.

Multinomial in Algebra Glossary :

An algebraic expression containing more than three unlike terms is called a multinomial.

Examples:

i) 2x + 3⁄x + 7xy - 5⁄y , ii) 4√x + 3x^{2} + 2x^{3} + 9, iii) x + 6xy^{2} + 7yx^{3} - x^{4}, iv) x^{2}√y + y + xy + 8. are all multinomials.

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An algebraic expression containing one or more more terms is called a polynomial, if every variable in it has only whole number ( 0 or positive integer ) powers.

Example:

2x^{4} + 2x^{3} is a polynomial with 2 terms.

So what is the difference between multinomial and polynomial?

The powers of the variables in multinomial (and also in monomial, binomial, trinomial) can have any real values (positive integers, negaitive integers, rational numbers, irrational numbers}.

where as The powers of the variables in polynomial can have only whole number powers.

Out of the Examples given above for multinomial,ONLY iii) is polynomial.

i),which is x + 3⁄x + 7xy - 5⁄y is NOT a polynomial. Because it has negative power terms. ( x and y in the denominator indicate theirpowers are -1. )

ii) and iv) are not polynomials because they have '√'which means the power is 1⁄2 which is not a wholenumber.

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