Question

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

Answer 1

Hint:
Here, we have to use the concept of coefficient. Coefficient of a variable is a number or multiplicative factor which is multiplied with the variable in the given expression. So by simply taking the variable term separate, we will get the coefficient of the variable for the given expression.

Complete step by step solution:
Given expression is\[{\rm{ - 13x}}{{\rm{y}}^{\rm{2}}}\]
 Here x is the variable for which we have to find the coefficient.
So, we have to separate the variable with the other multiplicative factors within the expression.
Therefore, expression becomes\[{\rm{( - 13}}{{\rm{y}}^{\rm{2}}}) \times ({\rm{x)}}\]
We can clearly see that \[{\rm{( - 13}}{{\rm{y}}^{\rm{2}}})\] is the multiplicative factor which is multiplied with the variable i.e. x and multiplicative factor is known as the coefficient of the variable.

Hence, \[{\rm{ - 13}}{{\rm{y}}^{\rm{2}}}\] is the coefficient of x in the given expression i.e. \[{\rm{ - 13x}}{{\rm{y}}^{\rm{2}}}\]
So, option D is correct.

Note:
Variable is that entity which can take any value. Value of the coefficient can be constant or it can be a variable. If the value of the coefficient is only a number like 3 or -15 then it is a constant coefficient but sometimes the value of coefficient contains a variable which makes its value variable. As in our question the value of the coefficient is variable as it contains variable y which makes the coefficient value variable as y can take any value which result in a different value of coefficient. So, for the coefficient which contains any variable then its value depends upon the value of the variable. We can find the coefficient for any variable with some power i.e. \[{{\rm{x}}^2}{\rm{,}}{{\rm{y}}^{\rm{2}}}{\rm{ or }}{{\rm{x}}^3}{\rm{,}}{{\rm{y}}^3}\].