Sure, let's break down the process of factoring the polynomial [tex]\(6ab + 15a - 8b - 20\)[/tex] and identify its factors step-by-step.
1. Identify common patterns in the polynomial:
Recognize the polynomial: [tex]\(6ab + 15a - 8b - 20\)[/tex].
2. Group the terms for easier factoring:
Let's group the terms in pairs:
[tex]\[
(6ab + 15a) + (-8b - 20)
\][/tex]
3. Factor out common factors from each group:
From the first group [tex]\((6ab + 15a)\)[/tex], factor out [tex]\(3a\)[/tex]:
[tex]\[
3a(2b + 5)
\][/tex]
From the second group [tex]\((-8b - 20)\)[/tex], factor out [tex]\(-4\)[/tex]:
[tex]\[
-4(2b + 5)
\][/tex]
4. Combine the factored groups:
Notice that both groups contain a common factor [tex]\(\(2b + 5\)[/tex]\):
[tex]\[
3a(2b + 5) - 4(2b + 5)
\][/tex]
5. Factor out the common term [tex]\((2b + 5)\)[/tex]:
Extracting the common term, we get:
[tex]\[
(3a - 4)(2b + 5)
\][/tex]
Thus, after factoring the polynomial [tex]\(6ab + 15a - 8b - 20\)[/tex], we identify its factors as:
[tex]\[
(3a - 4)(2b + 5)
\][/tex]
So, the correct answer is:
b. [tex]\((3a - 4)(2b + 5)\)[/tex]
