Algebraic Expressions 2

Let us now see some mathematical vocabulary associated with algebraic expressions. We will learn these only so that referring to them becomes easy and accurate. A detailed study of these will have to wait until high school.

Polynomial

Many of the expressions that we saw in the previous chapter had more than one expression, which were added or subtracted. A collection of such expressions is called a Polynomial. (There are many precise conditions for a collection of algebraic expressions to be called a polynomial. But we will leave those details for higher classes)

An algebraic expression is called a “term” when it occurs along with other expressions. An example of an expression is x2y + ay3. Both x2y and ay3 are terms of a larger expression.

So a polynomial is made of several terms.

Degree of an Expression

Algebraic expressions are classified by their “degree”. This term “degree” is best explained through some examples.

Take an expression “x”. This can be thought of as “x1 ” where 1 is the exponent of x. The “degree” of “x” is equal to the value of its exponent, which in this case is 1. Hence this expression is said to be a “first degree” expression.

An expression “y2” & “z3 “ are said to be a “second degree” & “third degree” expressions respectively.

An expression “xyz” can be written as “x1 y1 z1”. The sum of the exponents of all the 3 variables in the expressions is 1 + 1 + 1 i.e 3. Hence “xyz” is said to be a “third degree” expression.

Now, we are ready to understand how the degree of an algebraic expression is decided. It is equal to the sum of all the exponents of the variables in that expression.

A constant can be thought of having a degree 0. Since addition of 0 does not change a total, the presence of a constant in an expression does not change the degree of an expression. It remains the total of the exponents of the variables in that expression. The degree of “5xy” or “axy” is 2. (Remember that “a” represents a constant with degree 0.

The term “x “ is a first degree expression. The degree of is 0 since “a” is a constant.

Let us see some more examples to strengthen our understanding.