6x^2-18x-60

Could someone help me out with this? I'm taking two math classes at once, so I'm getting things mixed up. The instructions for it say "factor completely, or state that the polynomial is prime"

Question

6x^2-18x-60

Could someone help me out with this? I'm taking two math classes at once, so I'm getting things mixed up. The instructions for it say "factor completely, or state that the polynomial is prime"

anonymous · Answer

So, this isn't a prime polynomial. It can be factored/simplified further. First, find the GFC of the equation. The GFC includes the largest number and highest degree of x that can be divided equally in the equation. Once you have the GFC, factor it out. Put the GFC as the first term and then divide each term by it.

anonymous · Answer

The GCF is 6, so it'd be like 6(x^2-3x-10) right?

anonymous · Answer

Yes, correct! The term in the parenthesis can be factored even further though. Which two numbers add up to -3 and multiply to -10?

anonymous · Answer

-5 and 2

anonymous · Answer

Those are your solutions to the equation, which is (x - 5)(x + 2). The fully simplified equation is 6(x - 5)(x + 2).

anonymous · Answer

Ohhh, that makes more sense than the answers I was coming up with! haha thank you!

anonymous · Answer

You're welcome