Question

Perform the indicated division of polynomials by monomials.
$\dfrac{{12{x^3} - 24{x^2}}}{{6{x^2}}}$

Answer 1

Hint: For solving this type of question we will first separate the term of the polynomial and will divide each term of it using the monomials. And in the end, we have the solution which will be the division of polynomials by monomials.

Complete step-by-step answer:
Here, in this question, we have the polynomials and are written as $12{x^3} - 24{x^2}$ and the monomials given by $6{x^2}$ . Therefore in terms of the division, it can be expressed mathematically as
$ \Rightarrow \dfrac{{12{x^3} - 24{x^2}}}{{6{x^2}}}$
Now we can observe here in this question that there are two terms in polynomial or we can say it the numerator and one term in the monomials and we can say it the denominator, so dividing them separately the equation formed will be equal to
$ \Rightarrow \dfrac{{12{x^3}}}{{6{x^2}}} - \dfrac{{24{x^2}}}{{6{x^2}}}$
Now we can see that the base is the same in each of the fractions, so each term will be simplified and the common term will get canceled out. So on solving it we will get the equation as
$ \Rightarrow 2x - 4$
Therefore, on dividing the polynomials by the monomials of $\dfrac{{12{x^3} - 24{x^2}}}{{6{x^2}}}$ , we get $2x - 4$ .

Note: This process can also be solved by taking out the LCM of the fractions and then the expression will be reduced into a single fraction. So then we will cancel out the like terms or we can say the same terms of the numerator and the denominator will cancel out. And in this way also we can solve the problem. So a polynomial is an expression in which there is more than one term and in monomials, there will only be one term.