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

Hint: This type of problem is based on the concept of factorisation. We have to first find the common terms from the expression and take it out of the bracket. Here, the common term is 3x. On taking 3x common, we get the given expression as a product of two functions of x, that are 3x and (1-3x). Hence, the factors of the given expression are obtained which is the required answer.

Complete step-by-step solution:
According to the question, we are asked to find the factor of \[3x-9{{x}^{2}}\].
We have been given the expression \[3x-9{{x}^{2}}\]. ---------(1)
First, we have to search for common terms.
We can write the expression as \[3x-{{\left( 3x \right)}^{2}}\] since \[{{\left( 3x \right)}^{2}}=9{{x}^{2}}\].
Here, we find that 3x is a common term.
On taking 3x common from the expression, we get
\[3x-9{{x}^{2}}=3x\left( 1-3x \right)\]
Now, we have converted the given expression as a product of two functions which are 3x and (1-3x).
When an equation is converted as a product of two functions, the two functions are called the factors of the equation.
Here, we find that 3x and (1-3x) to be the factors.
Therefore, the factors of the expression \[3x-9{{x}^{2}}\] are 3x and 1-3x.

Note: We can also solve this question by first taking x common from the expression and then take 3 common from the expression. The above method helps us to reduce the number of steps. Also, we should know the square of basic numbers to simplify the given function and find the final answer. We should not make calculation mistakes based on sign conventions, if any.