Question

How do you factor $3{{x}^{2}}-9x=0$ .

Answer 1

Now to factorize the given expression we will first simplify the expression by grouping common terms together. Hence if we take 3x common from the first terms and second term we will have a simplified expression which is nothing but factorization of the given expression.

Complete step by step solution:
Now we are given with a degree 2 polynomial in x.
Hence we have the given expression is a quadratic expression of the form $a{{x}^{2}}+bx+c$ where c = 0.
Now we want to factor the given expression.
Here to factor the expression means we want to write the given expression in terms of the factors.
Now let us first understand what the factors of polynomials are.
Now we know for numbers we say that the factors are all the numbers which can divide the given number.
Similarly factors of the polynomial are nothing but all the polynomials which divide the given polynomial.
Now again consider the given expression $3{{x}^{2}}-9x=0$
Now since there is no constant in the expression we can easily take 3x common from the two terms.
Hence taking 3x common from the first term and the last term we get,
$3x\left( x-3 \right)$
Now here $3x$ and $\left( x-3 \right)$ cannot be further factorized.
Hence we have the factors of the expression are 3x and x – 3.

Note: Now note that in the above expression we have x = 0 and x = 3 as the roots of the given expression. Hence we can say that if $x-\alpha$ is the factor of the expression then $x=\alpha$ is the root of the given expression.