## how to factor a 4 degree polynomial?

How would I solve an equation similar to this purely by using algebra, no graphing as I want exact answers. For those people that don't like helping people on homework, I have to say this. I have like 20 problems like this, and I just want to get down how to solve them.

x

btw the class is pre-calc

x

^{3}-3x>x^{2}+ 7btw the class is pre-calc

x^3 -3x>x^2 + 7

for these subtract x^2 from both sides to get

x^3-3x-x^2>7

now x(x^2-x -3)>7

now apply quadratic formula to get the answer but if you still have problem doing it you come surely come back

x

^{3}-3x > x^{2}+7x

^{3}-x^{2}-3x > 7 (don’t flip > b/c x^{2}can’t be neg.)x(x

^{2}-x-3) > 7x((1 ± √(1-4(-3)))/2)>7 (Pythagorean theorem used since x

^{2}-x-3 doesn’t factorx>14/(1± √13)

hope this helps.

inequality, so the answer is sort of fundamentally graphical, isn't it? We would plotted a curve y=x^{3}-x^{2}-3x-7, picked a point on either side of the curve to see which regions the inequality held for, and would have shaded or colored a number line appropriately. Pretty much as shown here.In this case, it looks like the equation only has one real root, "near" x=3 (from an online plotter)

I don't recall how to find roots of higher degree polynomials, and the online sites essentially say that it can't be done, other than numerically, or for trivial cases where you can "factor by guessing." I'm pretty sure that in my day, our problems would have had trivial factors. In this day of graphing calculators, I suspect that "finding roots by looking at the graph" is the expected method.

Numerical solution of higher polynomials is a computer science problem, and not a pre-calc problem, so I'm pretty sure you're not supposed to do that...

1. The example you have is a misprint in the book that will drive everyone nuts and can't be solved...

or

2. You may be on your way to proving e=mc

^{2.}