Question

The coefficient of \[x\] in \[ - 13x{y^2}\] is
A) 13
B) \[ - 13\]
C) \[13{y^2}\]
D) \[ - 13{y^2}\]

Answer 1

Hint:
Here we have to find the coefficient of the variable in the given term. Coefficient of any variable in the given term is the product of the remaining factors of that term. So we will first find the factors of the given term which is the product of two variables and a constant. The resultant factors will be equal to all variable and literal factors except the variable of which we have to find the coefficient.

Complete step by step solution:
Here we have to find the coefficient of the variable \[x\] in \[ - 13x{y^2}\].
First we will find all the factors of the term \[ - 13x{y^2}\].
There are two types of factors:-
1) Literal factors- Literal factors are factors which are variable.
2) Numerical factors- numerical factors are the factors which are constant in nature.
Here the coefficient of variable \[x\] in \[ - 13x{y^2}\] will be all the literal and numerical factors of \[ - 13x{y^2}\] except \[x\]. So this will be equal to \[ - 13{y^2}\].
Hence, the coefficient of variable \[x\] in \[ - 13x{y^2}\]is equal to \[ - 13{y^2}\].

Thus, the correct option is option D.

Note:
There are two types of coefficient:-
1) Numerical coefficient or simply coefficient- the numerical part of the coefficient is known as numerical coefficient.
2) Literal coefficient- the variable part of the coefficient is known as the literal coefficient.
In this question, the numerical coefficient of the variable \[x\] in \[ - 13x{y^2}\] is equal to -13 and the literal coefficient of the variable \[x\] in \[ - 13x{y^2}\] is equal to \[{y^2}\] but the overall coefficient of the variable \[x\] in \[ - 13x{y^2}\]is equal to \[ - 13{y^2}\]. Thus, the overall coefficient includes both numerical and literal coefficient.