Classifying Polynomials

CLASSIFYING POLYNOMIALS

A POLYNOMIAL can be classified by its number of terms and by its degree.

NUMBER OF TERMS

• A polynomial with 1 term is a MONOMIAL.

• A polynomial with 2 terms is a BINOMIAL.

• A polynomial with 3 terms is a TRINOMIAL.

• A polynomial with more than 3 terms is called a POLYNOMIAL.

DEGREE OF A MONOMIAL

• The degree of a monomial is the sum of the exponents of the variables.

• EXAMPLE - The degree of

   $a^2bc^3$ is 6 because  $2+1+3=6$   

DEGREE OF A POLYNOMIAL

• The degree of a polynomial is the highest exponent.

• Polynomials must be written in standard form before classifying by degree.

• A polynomial with one variable is written in standard form when its terms are written in descending order by degree.

 $5x^2-2x+1$  

The highest exponent is the 2 and there are 3 terms. 

This is a QUADRATIC TRINOMIAL.

 $3x^4+4x^2$  

The highest exponent is the 4 and there are 2 terms.

This is a QUARTIC BINOMIAL.

 $8x-1$  

While it appears there is no exponent, the x has an understood exponent of 1 and there are 2 terms.

Therefore, this is a LINEAR BINOMIAL.

 $5$  

There is no variable at all and there is one term.

Therefore, this is a CONSTANT MONOMIAL. 

Technically, $5$ could be written as  $5x^0$ because of the 
Zero Power Property of Exponents.

 $3x^2y^5$  

Since both variables are part of the same term, we must add their exponents together to determine the degree.   

2 + 5 = 7 so this is a 7TH DEGREE MONOMIAL.

Multiple Choice

Classify the polynomial by its number of terms.

 $7x^3+5x^2+1$  

• MONOMIAL

• BINOMIAL

• TRINOMIAL

• POLYNOMIAL

Multiple Choice

Classify the polynomial by its number of terms.

 $6y^5+9y^2-3y+8$  

• MONOMIAL

• BINOMIAL

• TRINOMIAL

• POLYNOMIAL

Multiple Choice

Classify the polynomial by its number of terms.

 $8x-4$  

• MONOMIAL

• BINOMIAL

• TRINOMIAL

• POLYNOMIAL

Multiple Choice

Classify the polynomial by its number of terms.

 $9x^2y+3$  

• MONOMIAL

• BINOMIAL

• TRINOMIAL

• POLYNOMIAL

Multiple Choice

Classify the polynomial by its number of terms.

 $12x^2$  

• MONOMIAL

• BINOMIAL

• TRINOMIAL

• POLYNOMIAL

Multiple Choice

Classify the polynomial by its degree.

 $7x^3+5x^2+1$  

• CONSTANT

• LINEAR

• QUADRATIC

• CUBIC

• QUARTIC

Multiple Choice

Classify the polynomial by its degree.

 $6y^5+9y^2-3y+8$  

• LINEAR

• CUBIC

• QUADRATIC

• QUARTIC

• QUINTIC

Multiple Choice

Classify the polynomial by its degree.

 $8x-4$  

• CONSTANT

• LINEAR

• QUADRATIC

• CUBIC

• QUARTIC

Multiple Choice

Classify the polynomial by its degree.

 $9x^2y+3$  

• CONSTANT

• LINEAR

• QUADRATIC

• CUBIC

• QUARTIC

Multiple Choice

Classify the polynomial by its degree.

 $12x^2$  

• LINEAR

• QUADRATIC

• CUBIC

• QUARTIC

• QUINTIC