Question

Simplify \[3{x^3} - 2{x^2}\].

Answer 1

Hint:We can simplify the given question through the factorization.The process Factorization simply means breaking a term or a polynomial into many smaller terms which upon multiplication yields the polynomial terms.Here we can perform factorization by taking the common terms outside if there are any, such that correspondingly the factors of this polynomial can be found.

Complete step by step answer:
Given, \[3{x^3} - 2{x^2}.........................\left( i \right)\]
Normally the process factorization is done by:
1. Making a perfect square
2. Grouping terms by taking common factors within them.
3. Simply taking common factors if there are any.
So on inspecting \[3{x^3} - 2{x^2}\] we observe that we cannot perform factorization by using the methods described in 1 or 2 since it’s not compatible with those processes.But also in \[3{x^3} - 2{x^2}\] we observe that the term ${x^2}$ is a common factor for both \[3{x^3}\;{\text{and}}\;2{x^2}\].

So for factoring \[3{x^3} - 2{x^2}\] we can use the process described in the 3rd point.
i.e. taking common factors from the terms in (i):
$ \Rightarrow 3{x^3} - 2{x^2} = {x^2}\left( {3x - 2} \right)...................\left( {ii} \right)$
Since the term ${x^2}$ is common to both we take ${x^2}$ from both the terms, also now there are no common terms and thus we can stop the process. Also on observing ${x^2}\left( {3x - 2} \right)$ we see that when ${x^2}$ is multiplied inside the bracket we get the parent polynomial term.

Therefore on factoring $3{x^3} - 2{x^2}$we get ${x^2}\left( {3x - 2} \right)$.

Note:While approaching a question one should study it properly and accordingly should choose the method to factorize or simplify the polynomial. Similar questions which cannot be expressed as perfect squares or cannot be grouped together should be approached using the same method as described above.