An expression that denotes an unknown quantity and multiplies another expression is called a factor of their product.
If you are a beginner, you must know what a factor really is in mathematics, and it can be understood from examples of the factors in arithmetic. If you have already learned its concept, let’s start learning the factors in higher level mathematics.
An expression represents an unknown quantity in advanced mathematics. In some cases, an expression multiplies one or more expressions and their product is also a math expression. Now, each mathematical expression is called a factor of their product because each expression divides the product completely.
Theoretically, you may confuse about the concept of factors in higher mathematics but the following simple examples help you to understand what a factor really is in advanced mathematics.
$x \times (x-4)$ $\,=\,$ $x^2-4x$
$x$ and $x-4$ are two math expressions, whereas the quantities of both expressions are not known mathematically. The product of them is equal to $x^2-4x$ and it is also a mathematical expression.
The expressions $x$ and $x-4$ are called the factor of $x^2-4x$ because the expressions $x$ and $x-4$ both can divide their product expression $x^2-4x$ completely.
The above example helped you to learn what a factor really is in higher mathematics and let’s look at another example to understand the concept of a factor much clear in mathematics.
$6(x+1)\sin{x}$ $\,=\,$ $6x\sin{x}+6\sin{x}$
The left-hand side expression can be written as follows in mathematics.
$\implies$ $6$ $\times$ $(x+1)$ $\times$ $\sin{x}$ $\,=\,$ $6x\sin{x}+6\sin{x}$
$6$ is a quantity in arithmetic form and its quantity is known, but $x+1$ and $\sin{x}$ are expressions in math form and they denote two unknown quantities. However, the product of $6$, $x+1$ and $\sin{x}$ formed a mathematical expression $6x\sin{x}+6\sin{x}$.
The number $6$, the expressions $x+1$ and $\sin{x}$ are called the factors of $6x\sin{x}+6\sin{x}$ because $6$, $x+1$ and $\sin{x}$ divide the expression $6x\sin{x}+6\sin{x}$ completely.
Now, you have clearly learned the concept of factors in higher mathematics from its definition and understandable examples.
A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.
Copyright © 2012 - 2025 Math Doubts, All Rights Reserved