Question

How do you factor completely $5{x^2} - 10x$?

Answer 1

Hint: In this question, we have been asked to factorize a given expression. We will start by taking the variable common out of the two terms along with the constant. This will give us two different factors. Keep each factor equal to$0$. This will give you two values of $x$.

Complete step by step answer:
We are given an expression and we have been asked to factorize it.
$ \Rightarrow 5{x^2} - 10x$ …. (given)
Now, we can see that $5x$ is common in both the terms. Let us take $5x$ common.
$ \Rightarrow 5x\left( {x - 2} \right)$
Now, we will keep each factor equal to $0$ in order to find the value of $x$.
$ \Rightarrow 5x = 0,x - 2 = 0$
Shifting to find the value of $x$,
$ \Rightarrow x = \dfrac{0}{5} = 0$ and,
$ \Rightarrow x = 2$

Hence, the required values of $x$ are $0$ and $2$.

Note: In this question, the expression that we were given to us did not have any constant value. But if it had a constant value, then what would have we done?
If the given expression had a constant value, it would have looked like $a{x^2} + bx + c = 0$ .
In this case, we would have used the following methods:
Splitting the middle term method – In this method, we find two numbers, p and q, such that $pq = ac$ and $p + q = b$. After this, we take a term common from the first two and last two factors. This gives us two factors. Then, we keep each factor equal to 0 and find the value of $x$.
Using the Quadratic formula – in this method, there is a formula designed which gives us two values of $x$ directly. The formula is - $x = \dfrac{{ - b \pm \sqrt D }}{{2a}}$, where $D = {b^2} - 4ac$ .