Write f(x)=x^4-12x^3+59x^22-138x+130 as a product of linear factors.
I listed the factors of 130 and used synthetic division, but none of the remainders came out to be 0. I graphed the function, but the function doesn't pass through the x-axis. I figured I could find the zeros and work out the problem that way, but obviously it didn't work. Does the function have imagenary numbers when factored? I'm stumped on this problem, so if any of you could help me by showing the answer and by providing the steps the took to obtain that answer, I'd really appreciate it! Thanks!
You are right.
I also graphed it and it does not cross the x-axis.
There is a minimum point at (3,4), and the graph rises sharply on either side of that point.
If the function is typed correctly, there is no way to express it as linear factors.
BTW, I am sure that third term should be 59x^2