Question

The degree of polynomial $p\left( x \right)={{x}^{2}}-3x-4{{x}^{3}}-6$ is?
(a) 2
(b) 1
(c) 3
(d) 6

Answer 1

Hint: First we need to understand the term polynomial and then we will see the meaning of the term degree of a polynomial. Now, to find the degree of the given polynomial $p\left( x \right)$ we have to check the highest power of the variable x present in the expression.

Complete step by step solution:
Here we have been provided with the polynomial $p\left( x \right)={{x}^{2}}-3x-4{{x}^{3}}-6$ and we are asked to determine the degree of this polynomial. First let us see the definitions of some common terms like polynomial and degree of the polynomial.
Now, in mathematics a polynomial is an expression containing variables and coefficients that involves arithmetic operations like addition, subtraction, multiplication, division and non negative exponentiation of variables which must be an integer. For example: - ${{y}^{3}}+y+3$, $xyz+{{x}^{2}}y+{{y}^{3}}$.
Now, the degree of a polynomial containing one variable is defined as the highest power of the variable present in the expression. Let us come to the question. We have the expression $p\left( x \right)={{x}^{2}}-3x-4{{x}^{3}}-6$. Clearly we can see that the highest exponent of the variable x is 3, therefore the degree of the polynomial is 3.

So, the correct answer is “Option c”.

Note: Note that In case multiple variables are present in the polynomial like in the example $xyz+{{x}^{2}}y+{{y}^{3}}$ then in that case we find the degree of the polynomial by finding the sum of exponents of each term present in the expression. The term in which the sum of exponents will be greatest will determine the degree of the polynomial.