Final answer:
The GCF of the expression 5x(8x-3) + 2(8x-3) is the binomial (8x-3). To factor it out, we rewrite the expression as (8x-3)(5x+2).
Step-by-step explanation:
The question asks to factor the Greatest Common Factor (GCF) out of the given expression 5x(8x-3) + 2(8x-3). To do this, first, we identify the GCF of the two terms. The GCF here is the entire binomial (8x-3), as it appears in both terms of the expression.
To factor out (8x-3), we can rewrite the expression as (8x-3) multiplied by the sum of the coefficients from both terms, which are 5x and 2. So, the expression becomes (8x-3)(5x+2). Now, the GCF (8x-3) is factored out, and we are left with the product of (8x-3) and (5x+2).