Math Doubts

Literal factor

A multiplying literal number or product of more literals in a term is called a literal factor.

Introduction

Every algebraic term is formed by the product of a number and a literal or product of more literals. The number and each literal in the term is in multiplication form to form the term by their product. Hence, each one of them is known as a factor. If the factor is in the form of a literal or product of two or more literals, then the factor is called a literal factor.

Example

$6xy$ is an algebraic term.

  1. The term can be written as $6 \times x \times y$. In this case, $6$, $x$ and $y$ are factors basically but $6$ is a number. So, it cannot be a literal whereas $x$ and $y$ are literals. Hence, they are called literal factors.
  2. The same term can also be written as $6 \times xy$. In this case, xy is a literal factor.

As per these two cases, $x$, $y$ and $xy$ are called literal factors for this term.

More Examples

Look at the following simple to difficult examples to understand the concept of literal factor completely.

$(1)\,\,\,\,\,\,$ $a$

$a$ is a literal basically but it is also an algebraic term. The letter $a$ is written once. So, it is considered as $1 \times a$.

In this case, $1$ and $a$ are factors but $1$ is a number whereas $a$ is a literal. Hence, the number $1$ is not a literal factor but $a$ is a literal factor.

$(2)\,\,\,\,\,\,$ $-b$

The letter $b$ is written once but a negative sign is displayed before this. Actually, it is known as $-1 \times b$.

The number $-1$ is an integer and not a literal. So, it is not a literal factor. However, $b$ is a literal. Therefore, the literal $b$ is called as a literal factor.

$(3)\,\,\,\,\,\,$ $\dfrac{2cd}{7}$
The term can be written as $\dfrac{2}{7} \times c \times d$. In this case, $\dfrac{2}{7}$ is not a literal factor because it is a rational number but $c$ and $d$ are literal factors.

The term can also be written as $\dfrac{2}{7} \times cd$. So, $cd$ is also a literal factor.

Therefore, $c$, $d$ and $cd$ are literal factors.

$(4)\,\,\,\,\,\,$ $5e^2f$

The term can be written as $5 \times e^2 \times f$. In this case, $5$ is a factor but a number. So, it cannot be a literal factor whereas the factors $e^2$ and $f$ are called literal factors.

The term can also be written as $5 \times e \times e \times f$. In this case, $e$ and $f$ are literal factors.

Alternatively, the term can also be written as $5 \times e \times ef$. In this example, $e$ and $ef$ are literal factors.

Similarly, the algebraic term can also be expressed as $5 \times e^2f$. So, the literal factor for this term in this case is $e^2f$.

According to these three cases, $e$, $f$, $e^2$, $ef$ and $e^2f$ are literal factors for this term.

$(5)\,\,\,\,\,\,$ $0.75g^3$

The term is written as $0.75 \times g^3$. In this case, $0.75$ and $g^3$ are factors but $0.75$ is not a literal factor because it is a decimal number whereas $g^3$ is a literal factor.

The term can be written as $0.75 \times g \times g^2$. In this case, $g$ and $g^2$ are the literal factors.

The term can also be written as $0.75 \times g \times g \times g$. In this case, $g$ is a literal factor.

As per these three cases, $g$, $g^2$ and $g^3$ are possible literal factors for this term.



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