Question

The value, when $12x\left( {8x - 20} \right)$ is divided by $4\left( {2x - 5} \right)$ is
A.$3x$
B.$7x$
C.$12x$
D.$13x$

Answer 1

Hint: We need to find the quotient when the algebraic expression $12x\left( {8x - 20} \right)$ is divided by $4\left( {2x - 5} \right)$. The expression $12x\left( {8x - 20} \right)$ will be the numerator and $4\left( {2x - 5} \right)$ will be the denominator. Solve the denominator to match the factors with the numerator factors. Cancel out the same factors to find the value.

Complete step-by-step answer:
We know that the expression $12x\left( {8x - 20} \right)$ is divided by $4\left( {2x - 5} \right)$. So, the numerator is $12x\left( {8x - 20} \right)$ and the denominator is $4\left( {2x - 5} \right)$.
 We need to find the value of $\dfrac{{12x\left( {8x - 20} \right)}}{{4\left( {2x - 5} \right)}}$. We can simplify the denominator to match the factor with the numerator factors.
 Use the distributive property of multiplication to simplify denominator.
$4\left( {2x - 5} \right) = \left( {8x - 20} \right)$
We can see that the factor $\left( {8x - 20} \right)$ is common in both the numerator and denominator. Now, cancel the common factor and solve.
$\dfrac{{12x\left( {8x - 20} \right)}}{{\left( {8x - 20} \right)}} = 12x$
Therefore, the value of $12x\left( {8x - 20} \right)$ is divided by $4\left( {2x - 5} \right)$ is $12x$.
So, option (C) is the correct answer.

Note: There is also an alternative method to solve this question. We can use a long division method to find the quotient when $12x\left( {8x - 20} \right)$ is divided by $4\left( {2x - 5} \right)$. Here, divisor is the monomial and dividend is binomial. Arrange the terms of dividend and divisor in descending order and then solve.
Make sure that the divisor and the dividend are correctly chosen otherwise it may lead to incorrect answers.