Defining Polynomials
Polynomial comes from the Greek word ‘Poly,’ which means many, and ‘Nominal’ meaning terms. Hence the collective meaning of the word is an expression that consists of many terms. Polynomials can be defined as algebraic expressions that include coefficients and variables. We define the degree of a polynomial with the help of variables, which are also known as indeterminates. One can perform various arithmetic operations on polynomial expressions like multiplication, subtraction, addition, etc.
Polynomials are classified into three types based on the number of terms. These three major types of the polynomial are:
Monomial: A monomial consists of only one term. This single term of a monomial should be a non-zero term. For example 8x.
Binomial: A binomial consists of two terms. For example 5x-2
Trinomial: A trinomial is a polynomial expression that consists of three terms. For example, 4x^2+3x+2.
Polynomials are one of the important topics of mathematics. Understanding polynomial expressions can be a bit tricky sometimes, but you need to adopt modern teaching methods to help students understand the concept of polynomials. You can visit cuemath.com, which is an online learning platform that helps students understand the concept of polynomials through modern methods like online games, puzzles, visual simulations, etc. Cuemath helps students enjoy the learning process and understand the concepts better.
Let us now understand the concept of the degree of a polynomial. We will also discuss how to find the degree of a polynomial.
Degree of a Polynomial
The greatest power in a polynomial expression is known as the degree of the polynomial equation. Thus, the degree of the polynomial is the indication of the highest exponential power in the polynomial. The coefficient of the polynomial has no role to play while determining the degree of the polynomial.
For example: In a polynomial 6x^4+3x+2, the degree is four, as 4 is the highest degree or highest power of the polynomial.
Steps to Find the degree of a Polynomial expression
Step 1: First, we need to combine all the like terms in the polynomial expression. i.e., the polynomial with all the like terms needs to be combined.
Step 2: Ignore all the coefficients in the polynomial expression.
Step 3: Now, the variable needs to be arranged in descending order.
Step 4: The largest power of the variable in the polynomial expression is the degree of the polynomial.
Degree of a Polynomial with More than One Variables
You will also see examples where polynomials come with one or more variables. In the case of a muti-variable polynomial, we find the degree by adding the powers of different variables in the polynomial expression. Now let us take an example of a polynomial that consists of two variables.
In the polynomial expression 7x^2y^4+9y^2+8, the degree of the polynomial can be determined by adding the exponent value of both x and y in the first term of the polynomial. So the degree here can be determined by adding the exponent of x, i.e., two, and the exponent of y, i.e., 4. Hence the degree of this polynomial is 2+4= 6. Therefore for this polynomial expression, the degree is 6.
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