Polynomial definitions

 

These are some definitions of polynomials and their terms. In Alberta, you usually learn polynomials in Grade 9.

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Table of Contents

Polynomial

Monomial

Binomial

Trinomial

Quadratic

Term

Degree of a Polynomial

Coefficient of a term

Constant

 


Polynomial

A polynomial is one term or the sum of two or more terms.

Example:

3x-1 is a polynomial,

1/x is not because 1/x=xnegative 1, and polynomials cannot be to a negative power.

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Monomial

 A monomial is a polynomial with only one term.

Example:

5yis a monomial,

2x + 1 is not a monomial.

2x is, -8/y isn't.

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Binomial

A binomial is a polynomial with two terms.

Example:

2y-y is, 3x is not.

1/2 x-3zy is, 1/a + 1/b is not.

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Trinomial

A trinomial is a polynomial with three terms.

Example:

1-2x-4y is, 2a + 4 is not.

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Quadratic

Of or pertaining to the second degree. (Example: x)

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Term

Any distinct quantity in a polynomial.

Example:

x is a term, 2 is not.

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Degree of a polynomial

The degree of a polynomial in a variable is the highest power of that variable.

Example:

xhas 2 degrees, x has 1 degree,

x+y has 5 degrees, and so on.

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Coefficient of a term

A coefficient of a term is a number or symbol multiplying a variable or an unknown quantity.

Example:

4x The 4 is the coefficient of the term x.

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Constant

A constant os a number or symbol that doesn't change.

Example:

2 is a constant,

x is n