Final answer:
The expression 8x^2 - 10x can be factored as 2x(4x - 5) by first finding the greatest common factor, which is 2x, and then dividing each term by 2x and expressing the original expression as the product of the common factor and the result from the division.
Step-by-step explanation:
To factor the expression 8x^2 - 10x, you should first look for the greatest common factor that each term shares. In this case, both terms in the expression have an x and can be divided by 2. This allows us to factor out 2x from each part of the expression.
Here is the factoring step by step:
Find the greatest common factor: Both terms are divisible by 2, and both have an x, so the greatest common factor is 2x.
Divide each term by 2x:
8x^2 / 2x = 4x
-10x / 2x = -5
Write the original expression as a product of the common factor and the result from the division: 2x(4x - 5).
Thus, the factored expression is 2x(4x - 5), which corresponds to option A.