Question

Find the degree of the following polynomial.
$\sqrt 3 {x^3} + 19x + 14$

Answer 1

Hint: The given polynomial is written in the standard format. To find the degree of a given
polynomial, we will observe the greatest power of a variable. Also observe the coefficient of the
greatest power of variable. The coefficient of the greatest power of variables should be non-zero.

Complete step-by-step answer:
Here the given polynomial is $\sqrt 3 {x^3} + 19x + 14$. In this polynomial, $x$ is the variable. In the
first term of a given polynomial, we can see that the coefficient is $\sqrt 3 $ and the power of $x$ is
$3$. In the second term, we can see that the coefficient is $19$ and the power of $x$ is $1$. The third term $14$ is constant so we can say that the power of $x$ is $0$. After writing coefficients and
powers of variable for every term, now we can say that the greatest power of variable $x$ is $3$ and
its coefficient is non-zero.
The degree of the polynomial is the greatest power of the variable. Therefore, the degree of the
polynomial $\sqrt 3 {x^3} + 19x + 14$ is $3$.
Additional information:
A polynomial which contains only one term is called a monomial. A polynomial which contains two terms is called a binomial. A polynomial which contains three terms is called trinomial. In this example, the given polynomial contains three terms. So, we can say that it is trinomial.

Note: The degree of the polynomial is always non-negative integer. To find the degree of polynomial,
first arrange the variable in descending order of their powers. This is called the standard format. In this example, the degree of the polynomial is $3$. So, we can say that it is a cubic polynomial.
Coefficients of the variable can be any real number.