Question

Find the dividend, if in a division process, the divisor, the quotient and the remainder are $\left( x+1 \right)$, $\left( 3x-2 \right)$ and 1 respectively.

Answer 1

Hint: We start solving the problem by recalling the relation between dividend, divisor, quotient, and the remainder in a division process. We then substitute the values of divisor, quotient, and remainder in this relation to proceeding through the problem. We then make subsequent calculations in this relation to get the required value of dividends.

Complete step-by-step solution:
According to the problem, we need to find the dividend if it is given that the divisor, quotient, and remainder is $\left( x+1 \right)$, $\left( 3x-2 \right)$ and 1.
Let us recall the relation between dividend, divisor, quotient, and the remainder in a division process. We know that the relation between dividend, divisor, quotient and remainder in a division process is given as $\text{dividend = }\left( divisor\times quotient \right)+remainder$.
So, we have dividend = $\left( \left( x+1 \right)\times \left( 3x-2 \right) \right)+1$.
$\Rightarrow $ dividend = $\left( 3{{x}^{2}}-2x+3x-2 \right)+1$.
$\Rightarrow $ dividend = $3{{x}^{2}}+x-1$.
We have found the dividend in the division process as $3{{x}^{2}}+x-1$.
$\therefore$ The dividend in the division process is $3{{x}^{2}}+x-1$.

Note: We should not confuse the terms that were present in the division process. We know that the dividend is the number that we are decided to divide and the divisor is the number that is used to divide the dividend. The quotient is the number that tells us how many parts that divisor divides the dividend and the remainder is the number that is left after the division process. We should not make calculation mistakes while solving this process. Similarly, we can expect problems to find the quotient, remainder by giving dividend and divisor.