Question

I need help with this question! I would really appreciate it if you would show the steps.

Answer 1

Yuck! That one looks nasty... it's actually not too bad. Let's take it in steps.

[1] Understand the question. We need to find the greatest common factor (GCF). The GCF is exactly what it says, it is the biggest factor in common to all the numbers being added or subtracted.

Once we find the GCF, it is easy to factor the expression (which is why they are forcing you to find it!).

[2] Let's start with the obvious numbers, 8, 2, and 10. What's the GCF of those?

Well... that has to be 2. I can factor anything bigger out because 2 itself would be gone!

[3] Let's move on to the variables... v^6, v^5, v^9. What's the GCF of those?

Well... I the most I can factor out is v^5.

[4] Putting it all together the GCF of this expression is 2v^5. Great!

[5] Now, we factor this out of the expression:
2v^5 (4v + 1 - 5v^4)

Check by multiplying it back:
2v^5 * 4v + 2v^5 * 1 - 2v^5 * 5v^4 = 8v^6 + 2v^5 - 10v^9
and we get back what we wanted.

The answer is 2v^5 (4v + 1 - 5v^4).