Question

State the degree of the polynomial \[9{x^3} - 7{x^2} + \dfrac{5}{3}{\left( {{x^2}} \right)^3}\] is
A.2
B.3
C.6
D.5

Answer 1

Hint: Here we have to find the degree of the given polynomial. Degree of polynomial is defined as the greatest power of the variable in a polynomial expression. First, we will simplify the given polynomial and then we will determine the degree of the given polynomial by using the definition and property of degree of polynomial.

Complete step-by-step answer:
Here we need to find the degree of the given polynomial i.e. \[9{x^3} - 7{x^2} + \dfrac{5}{3}{\left( {{x^2}} \right)^3}\] .
We will first simplify the given polynomial.
\[9{x^3} - 7{x^2} + \dfrac{5}{3}{\left( {{x^2}} \right)^3} = 9{x^3} - 7{x^2} + \dfrac{5}{3}{x^6}\]
Therefore, the polynomial is
\[ \Rightarrow p\left( x \right) = 9{x^3} - 7{x^2} + \dfrac{5}{3}{x^6}\]
On rearranging the terms of the polynomial, we get
\[ \Rightarrow p\left( x \right) = \dfrac{5}{3}{x^6} + 9{x^3} - 7{x^2}\]
We can see that the given polynomial is now in standard form. Here the highest power of variable \[x\] is 6 here.
From the definition of degree we know that the highest power of the variable in a polynomial expression is the required value of the degree.
Therefore, the degree of the given polynomial is equal to 6.
Hence, the correct option is option C.

Note: A polynomial is defined as the algebraic expression which consists of variables, coefficients and constants. Other name of the variable is called indeterminate. A polynomial can have any number of terms but the terms of a polynomial can’t be infinite. The degree of polynomial is the highest power of the variable present but not the highest power of coefficients.
There are three types of polynomial which are classified on the basis of the number of terms:-
Monomial: Monomial is defined as the polynomial expression which contains only one term.
Binomial: Binomial is defined as the polynomial expression which contains two terms.
Trinomial: Trinomial is defined as the polynomial expression which contains three terms.