To identify the factors of the expression [tex]\(6ab - 8a + 21b - 28\)[/tex], let's go through the factorization step by step.
First, take a look at the given expression:
[tex]\[6ab - 8a + 21b - 28\][/tex]
### Step 1: Group the terms to find common factors
We can group the terms in pairs to factor by grouping:
Group 1: [tex]\(6ab - 8a\)[/tex]
Group 2: [tex]\(21b - 28\)[/tex]
### Step 2: Factor out the greatest common factor (GCF) from each group
From the first group, [tex]\(6ab - 8a\)[/tex]:
- The GCF of [tex]\(6ab\)[/tex] and [tex]\(-8a\)[/tex] is [tex]\(2a\)[/tex].
- Factor [tex]\(2a\)[/tex] out:
[tex]\[6ab - 8a = 2a(3b - 4)\][/tex]
From the second group, [tex]\(21b - 28\)[/tex]:
- The GCF of [tex]\(21b\)[/tex] and [tex]\(-28\)[/tex] is [tex]\(7\)[/tex].
- Factor [tex]\(7\)[/tex] out:
[tex]\[21b - 28 = 7(3b - 4)\][/tex]
### Step 3: Combine the factored expressions
Now we have:
[tex]\[6ab - 8a + 21b - 28 = 2a(3b - 4) + 7(3b - 4)\][/tex]
Notice that both groups contain a common factor [tex]\((3b - 4)\)[/tex]. We can factor this out:
[tex]\[(2a + 7)(3b - 4)\][/tex]
Thus, the factors of [tex]\(6ab - 8a + 21b - 28\)[/tex] are:
[tex]\[\boxed{(2a + 7)(3b - 4)}\][/tex]
So, the correct answer is [tex]\((2a + 7)(3b - 4)\)[/tex].
