SOLUTION: X4-11x3+24x2 =? I understand that x2 is the highest common factor but am unsure of how to write this one out?

Question 729467: X4-11x3+24x2 =?
I understand that x2 is the highest common factor but am unsure of how to write this one out?
Answer by erika514(39) (Show Source): You can put this solution on YOUR website!
Hi,
You are absolutely right with your greatest common factor. That is our first step to this problem. Now we need to factor out to find what is left in the parentheses. When we do this we should get (x2-11x+24). We now have x2(x2-11x+24). We are not finished yet though. We can factor what is inside of the parentheses. When we factor x2-11x+24, we get (x-3)(x-8) and we stick the x2 in front of the two factored binomials. We can check our answer to make sure it is right. So when we factor (x-3)(x-8) using FOIL(first, outer,inner, last), we multiply x and x to get x2,-8 and x to get -8x, -3 and x to get -3x, and -3 times -8 to get 24. So we get x2-11x+24 once we simplify, which is our original equation in the parentheses. Our final step to check is to multiply each value by x2, our greatest common factor to make sure we get our first equation when we started. So, when we multiply 24 times x2 we get 24x2, when we multiply -11x times x2 we get -11x3 and when we multiply x2 times x2 we gwet x4. Our problem checks out, so our final answer to our problem is x2(x-3)(x-8). Good luck and let me know if you have any more questions. :)
P.S. I'll be happy to help with any more questions you or your friends may have. Just send me a message with any questions. :)
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