Question

How do you factor completely:- $2{{x}^{3}}+6{{x}^{2}}$?

Answer 1

Hint:Factorisation is a method of expressing or writing a given number in the form of the product of other numbers. The numbers present in the product are called as factors of the original number.

Complete step by step answer:
Let us first understand what is meant by the term factorisation.Factorisation is a method of expressing or writing a given number in the form of the product of other numbers. The numbers present in the product are called as factors of the original number. For example, the number 6 can be written in the form of the product of the numbers 2 and 3.
i.e. $6=3\times 2$.
Here, 3 and 2 are the factors of 6.

The method of factorisation can also be used for expressions containing variables.
Here, the expression is given as $2{{x}^{3}}+6{{x}^{2}}$ …. (i).
In the expression (i) we can see that the two terms have the term ${{x}^{2}}$ in common.
Therefore, the expression (i) can be written as $2{{x}^{3}}+6{{x}^{2}}={{x}^{2}}\left( 2x+6 \right)$.
Here, we can write the ${{x}^{2}}$ term as ${{x}^{2}}=x.x$
Therefore, the given expression $2{{x}^{3}}+6{{x}^{2}}$ can be factored to $2{{x}^{3}}+6{{x}^{2}}=x.x\left( 2x+6 \right)$.

Hence, the factors of the expression $2{{x}^{3}}+6{{x}^{2}}$ are x and $\left( 2x+6 \right)$.

Note:The number of factors of a given expression are always less than or equal to the highest power of the variable in the expression. The highest power of a polynomial is called the degree of the polynomial. In this case, the degree of the polynomial is 3 and the number of factors are two.