Any algebraic expression will consist of numbers, operations, variables and a few special characters used in the field of mathematics. Since the sequence is formed using constants and variables, this formation is referred to as a mathematical expression.
Note that no algebraic expression is found to have equal signs or sides. Examples for algebraic expressions are 4x + 5y – 3, 2x – 5, 4×2 – 1xy + 6, 6×3 – 2×2 + 6x – 1 and so on.
Lastly, the division of algebraic expression is the inverse proportion of multiplication. In the classification of algebraic expressions, there are 3 majors namely Monomial, Binomial and Polynomial.
We are going to understand each concept in short as described in the following sections.
Defining what is a Monomial and a Polynomial
Polynomial is the term used to denote the condition of P = 0. Here, this formula is also called the Polynomial equation or Polynomial expression. A polynomial can range anywhere between a trinomial, binomial or even possess ‘n’ count of terms.
When a polynomial formula has only 1 term, then this is said to be the monomial. 15xy is an example of a monomial term.
Binomial, as the name says, is a polynomial equation that has only 2 terms. To state an example, 1x + 4. Take the case of 2a(a+b) 2. This is also considered as a binomial expression due to the presence of binomial factors ‘a’ and ‘b’.
The Process of Dividing a Monomial by Another Monomial
Consider this division of polynomial expression 12a3 ÷ 4a. Here, the terms 4a and 12a3 are the 2 monomials of the equation. One can quickly simplify the equation by cancelling common values. This is quite similar to that of natural division in real numbers.
12a3 ÷ 4a = (12 × a × a × a) / 4 × a
After the cancellation process, we will get 12a3 ÷ 4a = 3a2.
When a Monomial Divides a Polynomial
As we read before, a polynomial equation can have multiple options such as 2, 3 or ‘n’. For this condition, we are considering a trinomial. We will take a monomial “3a” and then divide it using the polynomial equation “(6a3 + 7a2 + 9a)”.
(6a3 + 7a2 + 9a) ÷ 3a
Take only the common factors from the equation and for our case, 3a is the common value. So the equation will note become:
(6a3 + 7a2 + 9a) = 3a (2a2 + 7/3a + 3)
Start dividing the complete set by the monomial 3a.
(6a3 + 7a2 + 9a) ÷ 3a = 3a (2a2 + 7/3a + 3) / 3a
Upon cancellation of the terms 3a and 3a from the denominator and the numerator, we will get:
(6a3 + 7a2 + 9a) ÷ 3a = (2a2 + 7/3a + 3)
Hence, we divided a polynomial expression using a monomial term. Finally, we are about to learn the division of algebraic expression between 2 different polynomial values as given below.
Division Operation Between 2 Polynomials
We will consider this case using simple numbers for a better understanding. Take 2 separate polynomial figures and divide them.
(6a2 + 12a) ÷ (a + 2)
Did you notice that the above 2 polynomials are in the monomial form? Now, pick the common factors, which is 6a, and the equation becomes:
(6a2 + 12a) = 6a (a + 2)
As you might have guessed, divide the complete set with the monomial (a + 2).
(6a2 + 12a) ÷ (a + 5) = 6a (a + 2) / (a + 2)
By cancelling the common terms (a +2), we get (6a2 + 12a) ÷ (a + 5) = 6a
Thus, we formed a proper equation, resulting in a monomial value.
