Page 83 - Math Course 2 (Book 1)

Degree of a Polynomial

Arrange Polynomials in
MO. 3 - L3b
Ascending Order
Degree of a Polynomial:

Arranging Terms Examples

Vocabulary A-Z Arrange the terms of 16 + 14x + 2x – x so that
3
2
Let us learn some vocabulary the powers of x are in ascending order.
3
16 + 14x + 2x – x 2
1
0
3
0
= 16 + 14x + 2x – x 2 x = 1
Degree of a Monomial

2
3
16 + 2x – x + 14x
The degree of a monomial is the sum of the Answer
exponents of all its variables. 0 < 1 < 2 < 3
Monomial Degree Arrange the terms of 7y + 4x + 2xy – x y so that
3
2
2 2
3
8y 4 4 the powers of x are in ascending order.
3a 1 7y + 4x + 2xy – x y
3
3
2
2 2
2 3
–2xy z 1 + 2 + 3 or 6
2 2
2
1 3
3
= 7y + 4x + 2x y – x y x = x 1
7 0
2
2 2
3
3
Degree of a Polynomial Answer 7y + 2xy – x y + 4x
0 < 1 < 2 < 3
is the greatest degree of any term in the polynomial.
To f nd the degree of a polynomial, you must f nd the
degree of each term. Arrange Polynomials in
Descending Order
Terms Degree of Each Term
5mn² 3 Examples
2
2 3
–4x y , 3x , 5 5, 2, 0
2
3
3
2
3a, 7ab, –2a b, 16 1, 2, 3, 0 Arrange 8 + 7x – 12xy – 4x y so that the powers
of x are in descending order.
2
3
3
8 + 7x – 12xy – 4x y
Let’s Begin
0
0
1 3
2
3
= 8 + 7x – 12x y – 4x y x = 1 and x = x 1
2
3
3
Degree of a Polynomial Answer – 4x y + 7x – 12xy + 8
3 > 2 > 1 > 0
Example
Find the degree of each polynomial.
Degree of Each Degree of
Polynomial Terms
Term Polynomial
a. 12 + 5b + 6bc + 8bc 2 12 , 5b , 6bc , 8bc 2 0, 1, 2, 3 3
2
2
b. 9x –2x – 4 9x –2x – 4 2, 1, 0 2
2 5
2 5
c. 14g h j 14g h j 8 8
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