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Degree Of A Polynomial And Its Various Underlying Concepts

Polynomial is a dedicated concept of mathematics. Apart from polynomials, the degree of a polynomial is also a crucial concept of mathematics that is taught to students in classes. The degree of a polynomial is known for identifying the number of solutions of a function. One can identify the number of solutions of a function through the use of the concept of the degree of a polynomial. Moreover, it is explained as the highest exponential power of an equation. A degree of a polynomial can also be explained as the number of times a given function crosses the X-axis when plotted on a graph.

Let’s dive deep into the concept of the degree of a polynomial and understand it with greater efficiency.

As explained before, the degree of a polynomial is explained as the greatest exponential power of a polynomial equation. However, only the exponential power of variables is taken under analysis. The coefficients are ignored for arriving at the value of the degree of a polynomial equation. For example, consider ‘m’ as the highest power of a variable X in a polynomial equation. Therefore, the degree of a polynomial is considered to be ‘m’.

5x^5−43x^3+3x−6 is a polynomial equation. 5x^5 is the term in the polynomial equation with the highest power of the variable X. As the highest exponent of the polynomial equation is 5, the degree of a polynomial, therefore, arrives at 5. For finding the value of the degree of a polynomial, only the variable is considered instead of a constant.

For example, in the equation 4x^2+3x− π^3, the exponential power of the constant is 3, and of the term, 4x^2 is 2. However, the real value of the degree of a polynomial is considered to be 3 as the constant is not considered for the same.

Degree of Zero Polynomial and Constant Polynomial:

The zero polynomial is defined when all the coefficients of an equation are equal to 0. Therefore, in such a case the degree of a zero polynomial is arrived at zero, negative, or is considered to be undefined. On the other hand, in the case of a constant polynomial, the degree is considered to be zero as there is no variable in the polynomial equation. For example, in polynomial equation 7, the degree is arrived at 0 due to the absence of any variable i.e., ‘x’.

Degree of a Polynomial Equation with more than One Variable:

In the case of a polynomial equation with more than one variable, the degree of a polynomial is arrived at by adding the values of exponents of every variable. For example, in the equation, 56x^5 + 7x^3y^3 + 2xy.

  • 56x^5 has a degree of 5.
  • 7x^3y^3 has degree 6. Since the exponent or variable x is 3 and that of y is 3 and the sum is 6, the degree arrives at 6
  • 2xy has the variable 2 arrived at adding the value of exponential power of x and y which 1+1 = 2.

Therefore, the degree of a polynomial is 6.

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