Question

Drag each description to the correct location on the table. Each description can be used more than once. Classify each polynomial based on its degree and number of terms

Answer 1

Part 1)
`5x^(3) -8x` ----> Is a cubic Polynomial/ Is a binomial

Part 2)
`-6-x^(5) -3x^2` --->Is a quintic (5th Degree) Polynomial/ Is a trinomial

Part 3)
`(1/3)x^4` ----> Is a quartic (4th Degree) Polynomial/ Is a monomial

Part 4)
`(6/7)x+1` ----> Is a linear Polynomial/ Is a binomial

Part 5)
`-0.7x^2` -----> Is a quadratic Polynomial/ Is a monomial

Explanation:

we know that

Polynomials can be classified in two different ways - by the number of terms and by their degree

The degree of a polynomial is calculated by finding the largest exponent in the polynomial

The polynomial is classified by the number of terms as:

1) The polynomial with only one term is called monomial

2) The polynomial with two-term is called binomial

3) The polynomial with three-term are called trinomial

4) The polynomial containing only the constant term is a constant polynomial

5) If the expression contains more than three terms, then the expression is called a Polynomial

Part 1) we have

`5x^(3) -8x`

Name using Degree

The largest exponent in the polynomial is 3

so

Is a cubic Polynomial

Name using number of terms

The polynomial has only two terms

so

Is a binomial

Part 2) we have

`-6-x^(5) -3x^2`

Name using Degree

The largest exponent in the polynomial is 5

so

Is a quintic (5th Degree) Polynomial

Name using number of terms

The polynomial has only three terms

so

Is a trinomial

Part 3) we have

`(1/3)x^4`

Name using Degree

The largest exponent in the polynomial is 4

so

Is a quartic (4th Degree) Polynomial

Name using number of terms

The polynomial has only one term

so

Is a monomial

Part 4) we have

`(6/7)x+1`

Name using Degree

The largest exponent in the polynomial is 1

so

Is a linear Polynomial

Name using number of terms

The polynomial has only two terms

so

Is a binomial

Part 5) we have

`-0.7x^2`

Name using Degree

The largest exponent in the polynomial is 2

so

Is a quadratic Polynomial

Name using number of terms

The polynomial has only one term

so

Is a monomial