Question

What is the difference between a monomial, binomial and polynomial?

Answer 1

Hint: A monomial is a type of polynomial that contains only one term after simplification. Binomial is a type of polynomial that will have only two terms after simplification. Trinomials are polynomials that have only three terms after simplification. In each case, the terms can be constants, variables, integers, product or even exponents but positive exponents only.

Complete step-by-step solution:
Let us first see what a monomial is. A monomial is a type of polynomial that contains only one term after simplification. The one term in the monomial can be a constant, a variable, an integer, a product or even exponents but positive exponents only. For example, let us consider a function $f\left( x \right)=2x$ . This function is a monomial since there is only one term. Let us consider a function $f\left( x \right)=x{{y}^{-1}}$ . We can see that this function has only one term but with a negative exponent. Hence, we cannot call this a monomial. Similarly, we cannot state the function $f\left( x \right)=\dfrac{2}{x}$ a monomial. But, we can call $f\left( x \right)=\dfrac{2}{5}$ as a monomial since $\dfrac{2}{5}=0.4$ is a number. We cannot call $f\left( x \right)={{\left( 5.2 \right)}^{-\dfrac{3}{5}}}$ a monomial since the power is negative and a fractional one. Thus, we can say that monomials cannot have fractional or negative exponents and variables in the denominator.
Now, let us see what binomial is. Binomial is a type of polynomial that will have only two terms after simplification. These terms can be constants, variables, integers, product or even exponents but positive exponents only. For example, let us consider $f\left( x \right)=5x+2$ . This is a binomial since only two terms are present. Similar to the monomial, binomials cannot contain fractional or negative exponents (or variables in the denominator).
Let us see what a trinomial is. Trinomials are polynomials that have only three terms after simplification. These terms can be constants, variables, integers, product or even exponents but positive exponents only. For example, let us consider a polynomial $2{{x}^{2}}-xy+{{y}^{4}}$ . This polynomial is a trinomial since only three terms are present. Here also, trinomials cannot contain fractional or negative exponents (or variables in the denominator).

Note: We have seen that monomial, binomial and trinomials cannot contain fractional or negative exponents. This is because polynomials cannot contain fractional or negative exponents. We can check which type of a polynomial is the given expression only after simplification.