Question

Write the coefficient of \[5{x^2}\] in the equation \[5{x^2} - 5x\].

Answer 1

Hint: Here in this question, we need to find the coefficient from the equation. Coefficient is generally termed as a constant written with a variable. Coefficient is also defined as the variable factor, numerical factor or a product of both numerical and variable factor. We will find all the factors of the term in order to find its coefficient.

Complete step-by-step answer:
In this question, we are required to find the coefficient of \[5{x^2}\] in the equation \[5{x^2} - 5x\].
To do this, we will first find out the factors of \[5{x^2}\], as then only the coefficient can be determined.
We see that the factors of \[5{x^2}\] are \[5,x,x\] and 1. 1 is taken here because it is the universal multiplicative identity and 1 is the factor of all the numbers and all the terms irrespective of their type.
Now, let us find the common terms between the factors and \[5{x^2}\].
We see that the common terms are \[5,x,x\]. The only common term is 1.

Hence, the coefficient of \[5{x^2}\] in the equation \[5{x^2} - 5x\] is 1.

Note: Here, we are asked to find the coefficient of \[5{x^2}\] which is a product of both numerical and variable factors. So, we will treat \[5{x^2}\] as one entity in order to find its coefficient. If instead of \[5{x^2}\], we were asked to find the coefficient of \[{x^2}\] then we will not treat 5 and \[{x^2}\] as one entity. Here 5 is the constant which is a numerical factor and hence, the coefficient of \[{x^2}\] would have been 5 and not 1. Therefore, we can say that the coefficients of \[{x^2}\] and \[5{x^2}\] are different. So, it is very important to observe what is asked in the question.