dentify the factors of 15ab + 35a − 6b − 14. (5a − 2)(3b + 7) (5a + 2)(3b − 7) (5a − 7)(3b + 2) (5a + 7)(3b − 2)

To identify the factors of the expression $15ab + 35a - 6b - 14$, we can follow these steps:

1. Break Down the Problem

We are tasked with factoring the polynomial $15ab + 35a - 6b - 14$. We need to group the terms strategically to make it easier to factor.

2. Relevant Concepts

Factoring involves looking for common factors in pairs of terms and applying the distributive property. We can use the grouping method to factor this polynomial.

3. Analysis and Detail

1. Group the terms: $(15ab + 35a) + (-6b - 14)$

2. Factor out the common factors in each group: $5a(3b + 7) - 2(3b + 7)$

3. Now we can factor out the common binomial $(3b + 7)$: $(3b + 7)(5a - 2)$

4. Verify and Summarize

We have factored the expression correctly as: $(5a - 2)(3b + 7)$ Now, we can verify by expanding: $(5a - 2)(3b + 7) = 15ab + 35a - 6b - 14$ The factorization is confirmed to be correct.

Final Answer

The factors of the expression $15ab + 35a - 6b - 14$ are $(5a - 2)(3b + 7)$.