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Identify the factors of [tex]$15ab + 35a - 6b - 14$[/tex].

A. [tex]$(5a - 2)(3b + 7)$[/tex]
B. [tex][tex]$(5a + 2)(3b - 7)$[/tex][/tex]
C. [tex]$(5a - 7)(3b + 2)$[/tex]
D. [tex]$(5a + 7)(3b - 2)$[/tex]

Sagot :

GinnyAnsweridn
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]
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