SOLUTION: This is the last problem on my review and I spent 3 hours at math lab tonight and didn't get quite finished. If possible could you please explain this problem to me. x^3

SOLUTION: This is the last problem on my review and I spent 3 hours at math lab tonight and didn't get quite finished. If possible could you please explain this problem to me. x^3 - 7x^2

Question 425389: This is the last problem on my review and I spent 3 hours at math lab tonight and didn't get quite finished. If possible could you please explain this problem to me.
x^3 - 7x^2 - 14x + 48 = 0
I know the answers are x = -3, 2, 8
But I don't understand how to work it out.
Thanks very much!
Shelby
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
There is a lot of brute-forcing involved in this problem. It is quite difficult to factor a cubic but you can use the rational root test to find a rational root and reduce it to a quadratic equation. There is also a cubic formula, but I doubt anyone can memorize it.

For example, suppose you find x=2 using the rational root test. Then you can divide using either long or synthetic division. You will obtain a quadratic equation with no remainder, then find that the roots of that equation are -3 and 8.
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