Literal coefficient

A factor which contains at least one literal, in product form of an algebraic term is called a literal coefficient of the remaining factor or factors.

Introduction

In algebra, an algebraic term is written as product of two or more factors in some cases. Each factor is multiplying the remaining factor or factors and each factor is known as the coefficient of remaining factor or factors in this case. If the coefficient contains at least one literal number, then the coefficient is called as the literal coefficient of remaining factor or factors.

Example

$4ax^2y$ is an algebraic term. It is split as product of two factors.

$\implies$ $4ax^2y \,=\, 4 \times ax^2y$

Basically, $4$ and $ax^2y$ are factors because they both are multiplying each other. In this case, $4$ is a number and it does not contain at least one literal number but the remaining factor $ax^2y$ has three literals $a$, $x$ and $y$.

Therefore, the factor $ax^2y$ is called as the literal coefficient of $4$.

Example

$6pq^2r^3$ is an algebraic term and it is split as product of three factors.

$\implies$ $6pq^2r^3$ $\,=\,$ $6p \times q^2r \times r^2$

1. $6p$ is literal coefficient of $q^2r$ and $r^2$ because the factor $6p$ has one literal number $p$.
2. $q^2r$ is literal coefficient of $6p$ and $r^2$.
3. $r^2$ is literal coefficient of $6p$ and $q^2r$.

Example

$-89lm^{28}$ is an algebraic term and it is split as product of two factors.

$\implies$ $-89lm^{28}$ $\,=\,$ $-89l \times m^{28}$

1. $-89l$ is literal coefficient of $m^{28}$.
2. $m^{28}$ is literal coefficient of $-89l$.

The three examples have cleared that if any factor in a product form of an algebraic term has at least one literal number, then the factor is called as the literal coefficient of the remaining factor or factors.