Degree of a polynomial
The degree of a polynomial is a very straightforward concept that is really not hard to understand
Definition: The degree is the term with the greatest exponent
Recall that for y
^{2}, y is the base and 2 is the exponent
Example #1:
4x
^{2} + 6x + 5
This polynomial has three terms. The first one is 4x
^{2}, the second is 6x, and the third is 5
The exponent of the first term is 2
The exponent of the second term is 1 because 6x = 6x
^{1}
The exponent of the third term is 0 because 5 = 5x
^{0}
What? 5x
^{0} = 5?
Well, anything with an exponent of 0 is always equal to 1
Thus, 5x
^{0} = 5 × x
^{0} = 5 × 1 = 5
Since the highest exponent is 2, the degree of 4x
^{2} + 6x + 5 is 2
Example #2:
2y
^{6} + 1y
^{5} + -3y
^{4} + 7y
^{3} + 9y
^{2} + y + 6
This polynomial has seven terms. The first one is 2y
^{2}, the second is 1y
^{5}, the third is -3y
^{4}, the fourth is 7y
^{3},
the fifth is 9y
^{2}, the sixth is y, and the seventh is 6
The exponent of the first term is 6
The exponent of the second term is 5
The exponent of the third term is 4
The exponent of the fourth term is 3
The exponent of the fifth term is 2
The exponent of the sixth term is 1 because y = y
^{1}
The exponent of the last term is 0 because 6 = 6x
^{0}
Since the highest exponent is 6, the degree of 2y
^{6} + 1y
^{5} + -3y
^{4} + 7y
^{3} + 9y
^{2} + y + 6 is 6
Write a polynomial for the following descriptions
1)
A binomial in z with a degree of 10
2)
A trinomial in c with a degree of 4
3)
A binomial in y with a degree of 1
4)
A monomial in b with a degree of 3
Anwers:
1)
2z
^{10} − 4
2)
c
^{4} + c
^{2} − 8
3)
y + 4
4)
b
^{3}
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
Degree of x
^{3}y
^{2}. Degree of this monomial = 3 + 2 = 5