Question

How do you factor \[12x-60\]?

Answer 1

Hint: This question belongs to the topic of algebra. In this question, we will factor \[12x-60\]. For solving this question, we will first find out the prime factorization of 12. After that, we will find the factorization of 60. After that, we will solve the further equation. After that, we will take common terms in the equation that can be taken. After solving some further equations, we will get our answer. After that, we will see an alternate method to solve this question.

Complete step by step answer:
Let us solve this question.
In this question, we have asked to find the factor of the term which is given in the question.
The term given in the question is in the following:
\[12x-60\]
Let us find out the prime factorization of 12.
\[\begin{align}
  & 2\left| \!{\underline {\,
  12 \,}} \right. \\
 & 2\left| \!{\underline {\,
  6 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}\]
We can write the prime factorization of 12 as \[2\times 2\times 3\times 1\]
Now, we will find out the factor of 60.
\[\begin{align}
  & 2\left| \!{\underline {\,
  60 \,}} \right. \\
 & 2\left| \!{\underline {\,
  30 \,}} \right. \\
 & 3\left| \!{\underline {\,
  15 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}\]
So, we can write the prime factorization of 60 as \[2\times 2\times 3\times 5\times 1\].
Now, we can write the term \[12x-60\] as
\[12x-60=2\times 2\times 3\times 1\times x-2\times 2\times 3\times 5\times 1\]
Now, taking \[2\times 2\times 3\] as common in the above equation, we can write
\[\Rightarrow 12x-60=2\times 2\times 3\times \left( 1\times x-5\times 1 \right)\]
The above equation can also be written as
\[\Rightarrow 12x-60=12\left( 1\times x-5\times 1 \right)\]
The above equation can also be written as
\[\Rightarrow 12x-60=12\left( x-5 \right)\]

Now, we have factored the term \[12x-60\]. The factor of the term \[12x-60\] is \[12\left( x-5 \right)\].

Note: We should have a better knowledge in the topic of algebra. We should have knowledge in finding prime factorization of any number. We can solve this question by an alternate method. For solving from the second method, we should know that 12 multiplied by 5 is 60. So, the term we have to solve is \[12x-60\].
We know that 60 can be written as 12 multiplied by 5. So, we can write the above term as
\[\Rightarrow 12x-12\times 5\]
Now, taking 12 as common in the above term, we can write
\[\Rightarrow 12\left( x-5 \right)\]
As we have got the same answer, so we can use this method too to solve this question.