Question

Write the degree of each of the following polynomial:
(a)$5{{x}^{3}}+4{{x}^{2}}+7x$
(b)$4-{{y}^{2}}$
(c)$5t-\sqrt{7}$
(d)3

Answer 1

Hint: First we are going to write the definition of degree and then we will use that definition to find the degree of each of the polynomials given and then that will be the final answer to this question.

Complete step-by-step answer:
Let’s first write the definition of terms:
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.
Now we are going to use this definition to find the degree of each of the given polynomials.
Let’s first find the degree of (a): $5{{x}^{3}}+4{{x}^{2}}+7x$
In this polynomial the highest power of x is 3,
Hence the degree of polynomial is 3.
Let’s first find the degree of (b): $4-{{y}^{2}}$
In this polynomial the highest power of y is 2,
Hence the degree of polynomial is 2.
Let’s first find the degree of (c): $5t-\sqrt{7}$
In this polynomial the highest power of t is 1,
Hence the degree of polynomial is 1.
Let’s first find the degree of (d): 3
In this polynomial there is no variable.
Hence the degree of polynomial is 0.
Hence we have found all the degrees of the polynomial using the definition of degree.

Note: Here students must understand the meaning of the degree of polynomial. And if there is no variable then the power of the variable is 0, hence it’s degree is 0. So, this part was a bit confusing so we must be careful.