ALGEBRA GLOSSARY : DEFINITIONS
WITH EXAMPLES OF MONOMIAL,
BINOMIAL, TRINOMIAL, MULTINOMIAL,
POLYNOMIAL, STUDY OF POLYNOMIALS

Please study
Algebra Terms before Algebra Glossary
if you have not already done so.

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, 6ab²c, 2a⁄b² is a monomial.

Binomial in Algebra :

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

Examples:

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

(ii) -3ab² + 9b²a is NOT a binomial.
Because the two terms are like terms.
You can see -3ab² + 9b²a = -3ab² + 9ab² = 6ab² is a single term.

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

(iv) a²b + 9ab²c is a binomial having two terms namely a²b and 9ab²c.

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) 4x² - 5y⁄2 + 3z² is a trinomial having three terms 4x², -5y⁄2 and 3z².

(iv) 2a + 3⁄b -4⁄c² is a trinomial having three terms 2a, 3⁄ b and - 4⁄c².

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 + 3x² + 2x³ + 9,
iii) x + 6xy² + 7yx³ - x⁴,
iv) x²√y + y + xy + 8.
are all multinomials.

Polynomial in Algebra Glossary :

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:

2x⁴ + 2x³ 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 their powers are -1. )

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

Polynomials is an important topic in Basic Algebra.

For studying about various aspects of them, go to

POLYNOMIALS

Algebra Formulas.

Algebra Factoring.

Factoring Special Products.

Factoring Trinomials.

Factoring Polynomials.

For studying to find the value of an
algebraic expression by substitution,
Go to

Algebra Substitution