Question

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

Answer 1

Given an expression. We have to factorize the expression. First, we will take out the common term from the expression. Then, check whether the equation is in simplified form.

Complete step-by-step answer:
We are given the expression $5{x^2} - 10x$. First, we will take out $5$ as a common term of the expression.
$\Rightarrow 5\left( {{x^2} - 2x} \right)$
Now, again the common term inside the bracket is $x$. So, we will take out $x$ as a common term.
$\Rightarrow 5x\left( {x - 2} \right)$
We can check the result by applying the distributive property to the expression. We will multiply each term inside the parentheses by the term $5x$.
$\Rightarrow 5x\left( x \right) - 5x\left( 2 \right)$
On simplifying the expression, we get:
$\Rightarrow 5{x^2} - 5 \times 2x$
$\Rightarrow 5{x^2} - 10x$
Thus, we get the given expression.

Thus, the factors of the expression is $5x\left( {x - 2} \right)$

Additional Information: The degree of the polynomial is defined as the highest exponent of the expression. Here, the degree of the polynomial is two. When we have to simplify the expression, the first thing we will do is to take out the common term from the expression. Then, simplify the remaining components of the expression. In the expression, factors are created to simplify the expression. If the factor of the expression is not possible, then it means the expression is already in its reduced form. The factors are used to determine the values at which the output of the function or expression will be zero.

Note:
In such types of questions students mainly don't get an approach on how to solve it. In such types of questions, students are mainly confused about which algebraic identity must be applied.