Question

Factorize \[7x - 42\]

Answer 1

Hint: In order to solve the question given above, you need to know what is factorization. It consists of writing a number as a product of several factors. It is usually smaller objects of the same kind. To solve this question, we will use two methods: 1) we will simply take out the common multiple. 2) we will individually find the factors of the two parts of \[7x - 42\] and then find the common factor.

Complete step by step solution:
We have to factorize \[7x - 42\] .
Method 1)
We have, \[7x - 42\] .
This can be written as:
 \[7x - 42 = \left( {7 \times x} \right) - \left( {7 \times 6} \right)\]
Now, we will take \[7\] as a common multiple.
We get:
 \[7x - 42 = 7\left( {x - 6} \right)\] .
So, our required answer is .
Method 2)
Now we will try another method to solve the same question.
We have: \[7x - 42\] .
Now,
 \[7x\] can be written as:
 \[7x = 7 \times x\]
Also, \[42\] can be written as:
 \[42 = 2 \times 3 \times 7\] .
(You can calculate the above result using L.C.M)
Now, we find that the only common factor in \[7x\] and \[42\] is \[7\] .
So, we can write \[7x - 42\] as: \[\left( {7 \times x} \right) - \left( {2 \times 3 \times 7} \right)\] .
We get:
 \[7x - 42 = 7\left( {x - \left( {2 \times 3} \right)} \right)\] .
The above equation can be written as:
 \[7x - 42 = 7\left( {x - 6} \right)\] .
So, we find that the factorization of \[7x - 42\] is \[7\left( {x - 6} \right)\] .
So, the correct answer is “ \[7\left( {x - 6} \right)\]”.

Note: While solving the questions similar to the one given above, you need to keep in mind that you can follow any one of the two methods given above. The answer derived from both the methods should be exactly the same. You can see that method 1) is quite simple and consumes less time whereas method 2) is a bit lengthy. You can choose the method you want to follow depending upon the marks that the question carries.