The degree of an equation is the maximum number of times any variable or variables are multiplied together in any single term.^{[1]} The degree of an equation is used to help decide how to solve an equation, or whether or not an equation has a solution.
To determine the degree of an equation, first eliminate any parenthesis by using the distributive property of multiplication over addition and subtraction. Take the equation:
When determining the degree of an equation, it is important to be able to recognize different terms. For more information on recognizing different terms see Term. The next equation shows an equation divided into terms:
Here is an example of an equation with two variables that is divided into terms:The degree of a single term is the sum of the exponents of any variables in the term. Start with the term 3x^{2}. The is only one variable in the term: x. The exponent of x is 2. So term 3x^{2} has a degree of 2.
Now look at the term 14x. There is no exponent showing, so what is the degree? To figure this out, use the property of an exponent of 1: a^{1} = a. The implied exponent of x is 1. So the term 14x has a degree of 1.
To find the degree of a term with more than one variable, add the exponents of each of the variables. The sum is the degree of the term. The degree of x^{2}y^{4} is 2 + 4 = 6. The degree of the term g^{3}h^{4}k^{2} is 3 + 4 + 2 = 9.
One more example. What is the degree of the term -3? Use another property of exponents: a^{0} = 1. Combine this with the property of multiplying by 1: 1·b = b. The term -3 can be written -3x^{0}. The degree of this term then is 0. The degree of any constant term is 0.
The degree of an equations is the largest degree of any term. In the equation
the degree of term 1 is 3. The degree of term 2 is 1. The degree of the constant term 3 is 0. The degree of the equation is the greatest of the degrees of the terms. This equation has degree 3.# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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