Question

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

Answer 1

Check for the common factor between each term of the expression, and then take the common factor out of the term then rewrite the expression in its factored form. Find common factors by splitting the terms into their factors.

Complete step by step solution:
In order to factorize an expression, we should firstly check for any common factor between all the terms of the expression, so now checking for common factors between the terms ${x^2}\;{\text{and}}\;5x$ by splitting them in their factors as following

We can write ${x^2} = x \times x\;{\text{and}}\;5x = 5 \times x$
We can see that there is a common factor between them which is equal to $x$

Now taking $x$ common from the given expression we will get
$= {x^2} - 5x \\\ = x(x - 5) \\\$
Therefore the required factored form of the expression ${x^2} - 5x$ is $x(x - 5)$

We should check our answer by performing the multiplication between resultant factors. So multiplying
$x$ with $x - 5$ , we will get
$= x \times (x - 5)$

Using the distributive property of multiplication to multiply the terms further
$= x \times x - x \times 5 \\\ = {x^2} - 5x \\\$

So we got the given expression after the multiplication of terms of the resultant factors. It means our factorization and result is correct.

Note: We can also solve this by sum product method for factorization of algebraic expressions. Sum product method can only be applied for quadratic polynomial expressions, it can be understood as a quadratic polynomial expression $a{x^2} + bx + c$ where $a,\;b\;{\text{and}}\;c$ are constant, can be factorized by splitting the middle term i.e. the coefficient of $x$ in such a way that the multiplication of the separated terms should be equal to product of $a\;{\text{and}}\;c$ and their sum should be equal to $b$ Try this method by yourself for this question. Hint: Take value of $c = 0$