Question

Classify each polynomial by degree and number of terms1. X^3 + 5x 2.X^2 - 2x - 13.5x^44. 6x^5 - 3x^2 + 7x + 95.-11x - 56. 4x^2 + 10

Answer 1

Recall that the degree of the polynomial is the highest power of the variable.

1)

`x^3+5x`
`The\text{ power of the variable in the term }x^3=3`

`The\text{ power of the variable in the term }5x=1`

3 is the highest number.

The degree of the polynomial is 3.

`x^3\text{ is the first term and 5x is the second term}`

The number of terms =2.

2)

`x^2-2x-1`

`The\text{ power of the variable in the term }x^2=2`

`The\text{ power of the variable in the term -2x}=1`

`The\text{ power of the variable in the term -1}=0`

2 is the highest number.

The degree of the polynomial is 2.

The number of terms =3.

3)

`5x^4`

`The\text{ power of the variable in the term }5x^4=4`

The degree of the polynomial = 4.

The number of terms =1.

4)

`6x^5-3x^2+7x+9`

`The\text{ power of the variable in the term }6x^5=5`

`The\text{ power of the variable in the term }-3x^2=2`

`The\text{ power of the variable in the term }7x=1`

`The\text{ power of the variable in the term }9=0`

5 is the highest number.

The degree of the polynomial =5.

The number of terms =3.

5)

`-11x-5`

`The\text{ power of the variable in the term }-11x=1`

`The\text{ power of the variable in the term }-5=0`

one is the highest number

The degree of the polynomial =1.

The number of terms =2.

6).

`4x^2+10`

`The\text{ power of the variable in the term 4}x^2=2`

`The\text{ power of the variable in the term }10=0`

2 is the highest number.

The degree of the polynomial =2.

The number of terms = 2.