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

Last updated date: 17th Jul 2024
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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.

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.