Question

A literacy campaign was organised by class IX girl students under NSS. Students made $x-5$ rows and $3x-4$ columns for the rally. Write the total number of students in the form of a polynomial.

Answer 1

Hint: We are given the number of rows and columns formed by the students. The total number of students participating in the rally can be found by multiplying the number of rows and the number of columns. We have a number of rows and columns. We will multiply these to obtain the polynomial in the variable $x$ to obtain the total number of students.

Complete step by step answer:
The number of rows formed by the students is $x-5$ and the number of columns is $3x-4$. We know that to obtain the total number of students in the rally can be found by multiplying the number of rows and the number of columns. This is true because we will either add the number of rows for number of column times or we will add the number of columns formed by students for number of row times. Therefore, we get the following formula,
$\text{total students}=\text{number of rows}\times \text{number of columns}$
Substituting the number of rows and number of columns in the above formula, we get
$\text{total students}=\left( x-5 \right)\times \left( 3x-4 \right)$
Multiplying the terms of the above equation, we get the following,
$\begin{align}
  & \text{total students}=3{{x}^{2}}-15x-4x+20 \\
 & \therefore \text{total students}=3{{x}^{2}}-19x+20 \\
\end{align}$
Hence, the total number of students is $3{{x}^{2}}-19x+20$.

Note:
 We should be familiar with the concept of counting the total number of elements using the number of rows and the number of columns. Multiplication of two numbers indicates the addition of one number for the number of times equal to the second number. It is useful to do the multiplication explicitly so that we can avoid making any minor mistakes and obtain the correct product of the factors.