To identify the factors of the expression [tex]\( 15ab + 35a - 6b - 14 \)[/tex], let's carefully analyze the expression and find its factorized form.
Given that we need to factor the expression [tex]\( 15ab + 35a - 6b - 14 \)[/tex], let's start by looking at common factors and possible groupings:
1. Group the terms in pairs:
[tex]\[ 15ab + 35a - 6b - 14 \][/tex]
Group the terms:
[tex]\[ (15ab + 35a) - (6b + 14) \][/tex]
2. Factor out the common factor from each group:
- From the first group [tex]\( 15ab + 35a \)[/tex], we can factor out [tex]\( 5a \)[/tex]:
[tex]\[ 5a(3b + 7) \][/tex]
- From the second group [tex]\( -6b - 14 \)[/tex], we can factor out [tex]\( -2 \)[/tex]:
[tex]\[ -2(3b + 7) \][/tex]
So now we have:
[tex]\[ 5a(3b + 7) - 2(3b + 7) \][/tex]
3. Notice that [tex]\( (3b + 7) \)[/tex] is a common factor:
We can factor [tex]\( 3b + 7 \)[/tex] out of the expression:
[tex]\[ (3b + 7)(5a - 2) \][/tex]
Thus, the expression [tex]\( 15ab + 35a - 6b - 14 \)[/tex] can be factorized as:
[tex]\[ (5a - 2)(3b + 7) \][/tex]
Therefore, the correct answer is:
[tex]\[ (5a - 2)(3b + 7) \][/tex]
