CLASSIFYING POLYNOMIALS

Determine if each expression is a monomial, binomial, trinomial, or not a polynomial.

Problem 1 :

 -4xy

Solution :

Number of terms :

It has one term

Name of the polynomial :

 Monomial

Problem 2 :

a² - 8

Solution :

Number of terms :

It has two terms

Name of the polynomial :

Binomial

Problem 3 :

 x/5

Solution :

Number of terms :

It has one term

Name of the polynomial :

Monomial

Problem 4 :

 7z^-1

Solution :

Number of terms :

It has one term, but negative exponent

Name of the polynomial :

It is not a polynomial

Problem 5 :

 b⁷

Solution :

Number of terms :

It has one term

Name of the polynomial :

Monomial

Problem 6 :

2m - 7

Solution :

Number of terms :

It has two terms

Name of the polynomial :

Binomial

Problem 7 :

x² + 3x - 4 - 5

Solution :

Number of terms :

It has four terms

Name of the polynomial :

Polynomial

Problem 8 :

5/2x – 3

Solution :

Number of terms :

It has two terms

Name of the polynomial :

Binomial

Problem 9 :

3y² - 6 + 7y

Solution :

Number of terms :

It has three terms

Name of the polynomial :

Trinomial

Problem 10 :

 3x + 8x – 5x²

Solution :

Number of terms :

It has three terms

Name of the polynomial :

Trinomial

Problem 11 :

 8x³y²z

Solution :

Number of terms :

It has one term

Name of the polynomial :

Monomial

Problem 12 :

 2a² + 3ab-5ba

Solution :

Number of terms :

It has three terms

Name of the polynomial :

Trinomial

Problem 13 :

9r + 11 – 5r²

Solution :

Number of terms :

It has three terms

Name of the polynomial :

Trinomial

Name each polynomial by degree and number of terms

Problem 14 :

−3 x⁵ − 10 x⁴ − x³ + 4 x

Solution :

Number of terms :

It has four term.

Degree of the polynomial :

Degree = 5

Name of the polynomial :

Quintic polynomial with four terms

Problem 15 :

7 n − 4

Solution :

Number of terms :

It has two terms.

Degree of the polynomial :

Degree = 1

Name of the polynomial :

Linear binomial.

Problem 16 :

−5 p⁴

Solution :

Number of terms :

It has one term

Degree of the polynomial :

Degree = 4

Name of the polynomial :

Quartic monomial

Problem 17 :

−10 k² − 10

Solution :

Number of terms :

It has two terms

Degree of the polynomial :

Degree = 2

Name of the polynomial :

Quadratic binomial

Problem 18 :

−9 m² − m

Solution :

Number of terms :

It has two terms

Degree of the polynomial :

Degree = 2

Name of the polynomial :

Quadratic binomial

Problem 19 :

8 x⁶ + 2 x + 5

Solution :

Number of terms :

It has three terms

Degree of the polynomial :

Degree = 6

Name of the polynomial :

Sixth degree trinomial

Problem 20 :

 k⁵

Solution :

Number of terms :

It has one term

Degree of the polynomial :

Degree = 5

Name of the polynomial :

Fifth degree monomial

Problem 21 :

− r

Solution :

Number of terms :

It has one term

Degree of the polynomial :

Degree = 1

Name of the polynomial :

Linear monomial

Write in Standard Form. Then name each polynomial by degree and number of terms.

Problem 22 :

−10 p²

Solution :

The given polynomial is already in the standard form.

Number of terms :

It has one term

Degree of the polynomial :

Degree = 2

Name of the polynomial :

Quadratic monomial

Problem 23 :

7 m² − m + 8 m⁴ + 6 m³

Solution :

7 m² − m + 8 m⁴ + 6 m³

Standard form :

Writing the polynomial from highest exponent to lowest exponent.

8 m⁴ + 6 m³ + 7 m² − m

Number of terms :

It has four terms

Degree of the polynomial :

Degree = 4

Name of the polynomial :

Quartic with four terms

Problem 24 :

7 m² − m + 8 m⁴ + 6 m³

Solution :

10 b³

Standard form :

10 b³

Number of terms :

It has one term

Degree of the polynomial :

Degree = 3

Name of the polynomial :

Cubic with one term

Problem 25 :

 −8 x⁴ + 2 x³ + 9 x⁵

Solution :

 −8 x⁴ + 2 x³ + 9 x⁵

Standard form :

9 x⁵  −8 x⁴ + 2 x³

Number of terms :

It has four terms

Degree of the polynomial :

Degree = 5

Name of the polynomial :

Quintic trinomial