To factor the given expression [tex]\(-4a + 2\)[/tex], we need to look for the greatest common factor (GCF) of the terms in the expression.
### Step 1: Identify the GCF
The terms in the expression [tex]\(-4a + 2\)[/tex] are [tex]\(-4a\)[/tex] and [tex]\(2\)[/tex]. Let’s break each term into its prime factors to find the GCF:
- [tex]\(-4a = -1 \cdot 2^2 \cdot a\)[/tex]
- [tex]\(2 = 2^1\)[/tex]
The common factor between these terms is [tex]\(2\)[/tex], as it is the highest number that divides both [tex]\(2\)[/tex] and [tex]\(-4\)[/tex].
### Step 2: Factor out the GCF
Next, we factor out the GCF, which is [tex]\(2\)[/tex], from each term in the expression.
[tex]\[
-4a + 2 = 2 \cdot (-2a) + 2 \cdot 1
\][/tex]
### Step 3: Rewrite the expression
Now, we can express the original expression as a product of the GCF and another binomial. We factor out [tex]\(2\)[/tex] from both terms:
[tex]\[
-4a + 2 = 2 \left(-2a + 1\right)
\][/tex]
### Conclusion
The factored form of the expression [tex]\(-4a + 2\)[/tex] is:
[tex]\[
2 \left(-2a + 1\right)
\][/tex]
