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.

x3 -3x>x2 + 7

btw the class is pre-calc

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rattlesnake4 years ago
Lets see how to solve inequalities

x^3 -3x>x^2 + 7
for these subtract x^2 from both sides to get

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

vanhill6 years ago
probably too late to hand this in as hw... but maybe it can help someone else.
x3-3x > x2+7
x3-x2-3x > 7 (don’t flip > b/c x2 can’t be neg.)
x(x2-x-3) > 7
x((1 ± √(1-4(-3)))/2)>7 (Pythagorean theorem used since x2-x-3 doesn’t factor
x>14/(1± √13)

hope this helps.
westfw7 years ago
Are you sure you're looking for the right sort of answer? I mean, it's an inequality, so the answer is sort of fundamentally graphical, isn't it? We would plotted a curve y=x3-x2-3x-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...
caitlinsdad7 years ago
It has been eons since I have done one, but does one treat the > sign like an = sign so you can do the same operation on both sides, like multipy by 7 then subtract x squared to get one side simplified. You should then see some kind of expression that you know how to factor with some basic equations like x+1 and x-1, something like that.
guyfrom7up (author)  caitlinsdad7 years ago
Well it just doesn't work out at the end, I forget how to get rid some of the constants at the end so you can make it equal zero
Any answer to this? After dusting off google for algebra lessons, 4th degree polynomials or something to the 4th power are usually unsolvable or expressed in algebraic expressions. What you have is a cubic expression where you need to find the factors and ranges to solve.

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


2. You may be on your way to proving e=mc2.
guyfrom7up (author)  caitlinsdad7 years ago
it's a worksheet, and there's a bunch of problems like that. I can just graph it on my calculator and find the x-intercepts. But that won't give me an exact fraction answer...
LinuxH4x0r7 years ago
I hate my calc class and I have no clue