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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.<\/p>\n
Note that no algebraic expression is found to have equal signs or sides. Examples for algebraic expressions are 4x + 5y \u2013 3, 2x \u2013 5, 4×2 \u2013 1xy + 6, 6×3 \u2013 2×2 + 6x \u2013 1 and so on.<\/p>\n
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.<\/p>\n
We are going to understand each concept in short as described in the following sections.<\/p>\n
Defining what is a Monomial and a Polynomial<\/p>\n
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 \u2018n\u2019 count of terms.<\/p>\n
When a polynomial formula has only 1 term, then this is said to be the monomial. 15xy is an example of a monomial term.<\/p>\n
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 \u2018a\u2019 and \u2018b\u2019.<\/p>\n
The Process of Dividing a Monomial by Another Monomial<\/p>\n
Consider this division of polynomial expression 12a3 \u00f7 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.<\/p>\n
12a3 \u00f7 4a = (12 \u00d7 a \u00d7 a \u00d7 a) \/ 4 \u00d7 a<\/p>\n
After the cancellation process, we will get 12a3 \u00f7 4a = 3a2.<\/p>\n
When a Monomial Divides a Polynomial<\/p>\n
As we read before, a polynomial equation can have multiple options such as 2, 3 or \u2018n\u2019. For this condition, we are considering a trinomial. We will take a monomial \u201c3a\u201d and then divide it using the polynomial equation \u201c(6a3 + 7a2 + 9a)\u201d.<\/p>\n
(6a3 + 7a2 + 9a) \u00f7 3a<\/p>\n
Take only the common factors from the equation and for our case, 3a is the common value. So the equation will note become:<\/p>\n
(6a3 + 7a2 + 9a) = 3a (2a2 + 7\/3a + 3)<\/p>\n
Start dividing the complete set by the monomial 3a.<\/p>\n
(6a3 + 7a2 + 9a) \u00f7 3a = 3a (2a2 + 7\/3a + 3) \/ 3a<\/p>\n
Upon cancellation of the terms 3a and 3a from the denominator and the numerator, we will get:<\/p>\n
(6a3 + 7a2 + 9a) \u00f7 3a = (2a2 + 7\/3a + 3)<\/p>\n
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.<\/p>\n
Division Operation Between 2 Polynomials<\/p>\n
We will consider this case using simple numbers for a better understanding. Take 2 separate polynomial figures and divide them.<\/p>\n
(6a2 + 12a) \u00f7 (a + 2)<\/p>\n
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:<\/p>\n
(6a2 + 12a) = 6a (a + 2)<\/p>\n
As you might have guessed, divide the complete set with the monomial (a + 2).<\/p>\n
(6a2 + 12a) \u00f7 (a + 5) = 6a (a + 2) \/ (a + 2)<\/p>\n
By cancelling the common terms (a +2), we get (6a2 + 12a) \u00f7 (a + 5) = 6a<\/p>\n
Thus, we formed a proper equation, resulting in a monomial value.<\/p>\n","protected":false},"excerpt":{"rendered":"
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