Consider the expression

Question

-10x⁴y+3x²y²-xy³+15y⁴-5

 

a)List each term, and state the coefficient and degree of each.

 

b)What is the degree of the polynomial?

 

Answer 1

To find the degree of a polynomial or monomial with more than one variable for the same term, just add the exponents for each variable to get the degree

The degree of the polynomial overall is the degree of the highest term

The coefficient is simply the number in front of the variable

 

We have -10x⁴y+3x²y² -xy³ +15y⁴-5
Degree of first term -10x⁴y is 4 + 1 = 5, coefficient -10

Degree of 2nd term 3x²y² is 2 + 2 = 4, coefficient 3

Degree of 3rd term -xy³ is 1 + 3 = 4, coefficient -1

Degree of 4th term 15y⁴ is 4, coefficient 15

Degree of last term -5 is 0  since -5 = -5x⁰, coefficient -5

 

Since the term with highest degree is 5 the overall degree of the polynomial is 5

 

Answer 2

-10x⁴y    coefficient:  -10    degree:  4 + 1 = 5

 

    3x²y²  coefficient:      3     degree:  2 + 2 = 4

 

-xy³        coefficient:     -1     degree:  1 + 3 = 4

 

15y⁴       coefficient:    15     degree:  4

 

-5x⁰       coefficient:     -5      degree:  0

 

degree of polynomial = degree of the term with highest degree = 5

Answer 3

a)

 

The term is the value that is separated by an operator such as plus and minus.

 

-10x⁴y  ,    3x²y²  ,    -xy³   ,    15y⁴   ,    and    -5x⁰

 

The coefficient is the constant of the variables.  These are

 

-10  ,    3    ,     -1       , 15         and        -5

 

 

b)

 

The degree of the polynomial is determined by the leading term's highest exponent. 

 

The leading term is -10x⁴y.

 

The degree is 4.