Question

Which of the following is/are polynomials ?
A.$3x{y^2}$
B.$2x + 5$
C.$5{x^3} + 4{x^2} + 5x + 1$
D.None of these

Answer 1

Hint: In this question we have to check which of the given options are polynomials. Before solving this question we should know the definition of polynomials. There are different types of polynomials such as: Monomial, Binomial and trinomial. So we will also check the terms in the respective given options and then get our answer.

Complete step-by-step answer:
As we know that polynomials are algebraic expressions that comprise of components which are added, subtracted or multiplied, where each term holds a variable or variables that are elevated to power and further which are multiplied by coefficient.
We know that monomials are the algebraic expressions that have one term.
As for example
$21{x^2}y,4t,2x + 5x$ are all monomials because all of these expressions contains only one term
In the first option we have $3x{y^2}$ is a monomial because it has one variable. So we can also call it a polynomial in one variable.
Now in the second option we have
$2x + 5$
The above expression is a binomial. It is a type of binomial with two unlike terms. We can also call this a linear polynomial. So this is also a polynomial.
In the third option we have
$5{x^3} + 4{x^2} + 5x + 1$
We can see that the above expression has four terms, so it is a polynomial with four terms or we can say it is a quadrinomial. It is also called a cubic polynomial.
So option (a) , (b) and (c) are polynomials because monomial, binomial and quadrinomial are types of polynomials.
Hence we can say that all the given options are polynomials.
So, the correct answer is “Option A,B and C”.

Note: We should note that if polynomials with four terms have the highest degree $3$ of a single variable, then it is a cubic polynomial.
The general form of cubic polynomial is
 $a{x^3} + b{x^2} + cx + d$ .
We should keep in mind that trinomial is a polynomial with three terms i.e.
 $6{x^3} - 5{x^2} - 3x$ .