Question

The product of a monomial and a binomial is a
(A) Monomial
(B) Binomial
(C) Trinomial
(D) None of these

Answer 1

Hint: A monomial is roughly speaking a polynomial which has only one term. Two definitions of a monomial may be encountered as a monomial , also called power product, is a product of powers of variables with nonnegative integer exponents. A binomial is a polynomial that is the sum of two terms, each of which is a monomial. It is the simplest kind of sparse polynomial after the monomials. First we take a monomial and a binomial and then find the product of them.

Complete step by step answer:
Monomial contains one term and binomial contains two terms.
If we multiply monomial and binomial we get two terms.
Hence the product of a monomial and binomial is a binomial.
e.g., Take a monomial ${x_1}$ and also take a binomial ${x_2} + {x_3}$ .
Now we find the product of them and we get
${x_1}({x_2} + {x_3})$
We multiply both the monomial and binomial function, and we get binomial
$ = {x_1}{x_2} + {x_1}{x_3}$
As example, we multiply two monomial function and we get binomial
Two monomial functions \[{a_1}\] and ${b_1}$
Multiply both the monomial, we get
${a_1} \times {b_1}$
$ = {a_1}{b_1}$
Therefore, we get the binomial function.
Above function is also a binomial therefore for all times if we multiply a monomial and a binomial, we get a binomial as a product of them.

Therefore option (B) is correct.

Note:
Only for the multiplication if we multiply a monomial and a trinomial then we get a trinomial as a product of them and so on. But if we change the operation then the result will change according to the operation. If we use the operation addition then if we add a monomial and a binomial then we get a trinomial as a result and so on.