How do you factor the expression \[27{x^2} - 111x + 12\] ?

Hint: We have to find the factor of the given expression \[27{x^2} - 111x + 12\] , factorization: It is the process where the original given number is expressed as the product of prime numbers. For this we have to calculate the prime factor of \[27{x^2} - 111x + 12\].

Complete step by step solution:
The given expression is as follow ,
\[27{x^2} - 111x + 12\] ,
We have to find the factor of the given expression.
factorization: It is the process where the original given number is expressed as the product of
prime numbers.
Therefore , Factorization of \[27{x^2} - 111x + 12\] :
\[
   = 27{x^2} - 108x - 3x + 12 \\
   = 27x(x - 4) - 3(x - 4) \\
   = (27x - 3)(x - 4) \\
 \]
Hence, we get the required result that is a factor of the given expression \[27{x^2} - 111x + 12\] .

Additional Information:
LCD: Lowest Common Denominator : Lowest common denominator can be found by multiplying the highest exponent prime factors of the denominator . the lowest common denominator is also known as Least common multiple and this can be calculated in two ways ; with the help of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor. Prime factorization: It’s the process where the original given number is expressed as the product of prime numbers.

Note: Questions similar in nature as that of above can be approached in a similar manner and we can solve it easily. The above question can also be done by simply listing all the possible factors of the given expression \[27{x^2} - 111x + 12\] . We must know that prime factorization is the process where the original given number is expressed as the product of prime numbers.