Question

Factorize the following: \[7x - 42\]

Answer 1

Hint: In this question, we need to factorize the function \[7x - 42\]. Use the prime factorization method to break the number into the product of prime numbers. In prime factorization, if the same prime numbers happen to occur more than once, then these numbers are written in exponential form.

Complete step-by-step answer:
Prime numbers are generally referred to as the number which can only be divided by the integer 1 and by itself. In other words, the numbers which are greater than 1 but are not the product of smaller numbers. When we factorize a prime number, then they will only have two factors 1 and the number itself.
The given function is \[7x - 42\] , so we factorize 7x and 42 simultaneously.
We can write the function \[7x\] as \[7 \times x\].
Now we factorize 42 as
\[
   7\underline {\left| {42} \right.} \\
   3\underline {\left| 6 \right.} \\
   2 \;
 \]
Hence we can write this as \[42 = 7 \times 3 \times 2\]
So by substituting these factors we can write
\[7x - 42 = 7 \times x - 7 \times 3 \times 2\]
Now take 7 as common term from the factors, so we get
\[
\Rightarrow 7x - 42 = 7\left( {x - 3 \times 2} \right) \\
   = 7\left( {x - 6} \right) \;
 \]
Hence the factor of \[7x - 42\]is \[ = 7\left( {x - 6} \right)\]

Note: Determining the factors through the prime factorization method is very essential as if the factors are not the prime number then, it may be possible that the answer will be wrong. Alternatively, this question can be solved by a long division method as well if the candidate is not comfortable with the above used table.