Question

How do you factor \[3{{x}^{3}}-9{{x}^{2}}\]?

Answer 1

Hint: In this problem, we have to find the factor of the given equation. We can take the common terms from the given equation, to find the factor. We know that the given equation has \[3{{x}^{2}}\] as the common term. We can take the common term outside and we will get the factor of the given equation. we can multiply the factors again to check whether the factors found are correct. We can also use algebraic formulas when the given equation is a perfect square equation.

Complete step by step solution:
We know that the given equation is,
\[3{{x}^{3}}-9{{x}^{2}}\]
We know that the given equation has \[3{{x}^{2}}\] as the common term.
We can now take the common term outside, we get
\[\Rightarrow 3{{x}^{2}}\left( x-3 \right)\]
We can now multiply the above factors to check whether the factors are correct,
\[\Rightarrow 3{{x}^{2}}\left( x-3 \right)=3{{x}^{3}}-9{{x}^{2}}\]

Therefore, the factors of the given equation \[3{{x}^{3}}-9{{x}^{2}}\] are \[3{{x}^{2}}\left( x-3 \right)\]..

Note: Students make mistakes while taking the common terms outside from the given equation. In order to check for the correct factors, we can again multiply for the given equation. We know that the given equation has \[3{{x}^{2}}\] as the common term. We can take the common term outside and we will get the factor of the given equation. we can multiply the factors again to check whether the factors found are correct. We can also use algebraic formulas when the given equation is a perfect square equation.