Question

How do you factor the expression $ 5x+25 $ ?

Answer 1

Hint: We know that factorization of any expression or number means the splitting of expression or a number in such a way that factors are written in the product form and multiplying the factors will restore the original expression or number. So, to factorize the given expression we have to write the expression in the multiplication form. As you can see that 5 is common in the expression so take it common and see what is left.

Complete step by step answer:
The expression given in the above problem that we have to factorize is as follows:
$\Rightarrow$ $ 5x+25 $
As you can see that 5 is commonly dividing with 5 in 5x and 25 in the above expression so we can take 5 out from the above expression and we get,
$\Rightarrow$ $ 5\left( x+5 \right) $
You might be thinking about how we have come to the above expression. The reason is we have firstly divided 5x by 5 and we get x and then we divide 25 by 5 and we get 5 and this is how we have got in the bracket as $ \left( x+5 \right) $.
1 is also a factor of $ 5\left( x+5 \right) $ so we can rewrite this expression as:
$\Rightarrow$ $ 5\left( 1 \right)\left( x+5 \right) $
Hence, we have factorized the given expression in the following way:
$\Rightarrow$ $ 5\left( 1 \right)\left( x+5 \right) $

Note:
You can check whether the factors that we have found are correct or not by multiplying these factors and see whether we are getting the original expression or not.
$\Rightarrow$ $ 5\left( 1 \right)\left( x+5 \right) $
Multiplying 5 with 1 will give us 5 and the above expression will become:
$\Rightarrow$ $ 5\left( x+5 \right) $
Now, multiplying 5 with x and then 5 with 5 we get,
$\Rightarrow$ $ 5x+25 $
As you can see that we are getting the same expression that is given in the above problem, This means that we have found the correct factors.