Certainly! Let's go through the process of rewriting the given expression step by step.
1. Given Expression:
The original expression provided is [tex]\( 12x - 8 \)[/tex].
2. Factorization:
We need to factorize the expression [tex]\( 12x - 8 \)[/tex]. Let's identify the common factor in both terms:
- The terms are [tex]\( 12x \)[/tex] and [tex]\( -8 \)[/tex].
- The greatest common divisor (GCD) of 12 and 8 is 4, since 4 is the largest number that can divide both 12 and 8 without leaving a remainder.
3. Rewriting the Expression:
We can divide both terms by this common factor 4:
[tex]\[
12x \div 4 = 3x
\][/tex]
[tex]\[
-8 \div 4 = -2
\][/tex]
By factoring out the common factor 4 from each term, we rewrite the expression as:
[tex]\[
12x - 8 = 4(3x - 2)
\][/tex]
4. Factors of the Expression:
When we factor [tex]\( 12x - 8 \)[/tex] into [tex]\( 4(3x - 2) \)[/tex], the elements we have factored out are:
[tex]\[
4 \quad \text{and} \quad (3x - 2)
\][/tex]
Hence, 4 and [tex]\( 3x - 2 \)[/tex] are both factors of [tex]\( 12x - 8 \)[/tex].
Thus, in the context of the equation, the factors of [tex]\( 12x - 8 \)[/tex] are [tex]\( 4 \)[/tex] and [tex]\( 3x - 2 \)[/tex].
