Factorise fully 12x-8
The correct Answer and Explanation is:
To fully factorize the expression ( 12x – 8 ), follow these steps:
Step 1: Find the greatest common factor (GCF)
To factor the expression, the first step is identifying the greatest common factor (GCF) of the two terms, ( 12x ) and ( 8 ).
- The coefficients of the terms are 12 and 8. The GCF of 12 and 8 is 4, because 4 is the largest number that divides both 12 and 8 evenly.
- The variable in the expression is ( x ), which only appears in the first term. Since ( x ) does not appear in both terms, it cannot be part of the GCF.
Thus, the GCF of ( 12x – 8 ) is 4.
Step 2: Factor out the GCF
Once we have the GCF (4), we factor it out from both terms:
[
12x – 8 = 4(3x – 2)
]
Step 3: Check the result
After factoring out the GCF, the expression inside the parentheses is ( 3x – 2 ). There are no further common factors in ( 3x – 2 ), meaning the expression is now fully factorized.
Final Answer:
[
12x – 8 = 4(3x – 2)
]
Explanation
Factoring is a key algebraic technique used to simplify expressions or solve equations. The process of factoring involves finding a common factor (either numerical or involving variables) in terms of an expression and “factoring it out” by dividing each term by the common factor.
In this example, the expression ( 12x – 8 ) is made up of two terms: ( 12x ) and ( 8 ). The first step in factoring is to find the greatest common factor (GCF), which is 4. By factoring out 4, we rewrite the expression in its simplest form, ( 4(3x – 2) ).
This step is crucial because factoring simplifies expressions, making it easier to manipulate or solve them in equations.