Question

How do you determine if $a-{{a}^{2}}$ is a polynomial and if so, how do you identify if it is a monomial, binomial or trinomial?

Answer 1

Hint: Here in this question we have been asked to determine if the given expression $a-{{a}^{2}}$ is a polynomial or not and also we need to identify if it is a monomial, binomial or trinomial. A binomial is a polynomial containing two terms only. A polynomial is defined as an expression in the form of ${{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+..............+{{a}_{1}}{{x}^{1}}+{{a}_{0}}{{x}^{0}}$ .

Complete step-by-step answer:
Now considering from the question we have been asked to determine if the given expression $a-{{a}^{2}}$ is a polynomial or not and also we need to identify if it is a monomial, binomial or trinomial.
From the basic concepts we know that a polynomial is defined as an expression in the form of ${{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+..............+{{a}_{1}}{{x}^{1}}+{{a}_{0}}{{x}^{0}}$ .
Hence the given expression $a-{{a}^{2}}$ is a polynomial since it can be expressed as $-{{a}^{2}}+a$ .
From the basic concepts we can say that a monomial is a polynomial containing a single term and similarly a binomial is a polynomial containing two terms only.
A trinomial is a polynomial containing three terms only.
As observing the given expression $a-{{a}^{2}}$ consists of two terms only.
Therefore we can conclude that the given expression $a-{{a}^{2}}$ is a polynomial and it is a binomial.

Note: While answering this type of questions we have to be sure with the simplifications that we are going to perform and the concepts that we are going to apply in between the steps in order to answer them. This is a very simple and easy question and can be answered accurately within a short span of time. Very few mistakes are possible in this type of question. Someone can confuse and consider that a binomial means an expression having degree two but it is wrong it is the definition of a quadratic.