Does x^3 + x^2 -1 factor? and if yes.... how?
Which method would you use?
The only rules that I know are the diff of two sqares, and sum and dif. of two cubes....
Are there any others that I should know of?
How exactly do you wish to factor it? Like (x-a)(x-b)(x-c), if so then one of your roots are irrational and you can't factor it with algebraic manipulation.
I wasnt referring to using diff of two sqares, and sum and dif. of two cubes on this problem... I just want to know if there are other methods that I should know for future reference.
No, it's not between 1 and 2.And as far as picking a root... that could take all day couldnt it? Im sure its between 1-2 but that could be any decimal between those points.
Your root is not rational, so you will need to use an iterative method.
Never learned that method. Should I know that?... Ive only taken algebra....
And how do you know that it is irrational?
Apparently not well enough, because you asked earlier:I know the rat zero therm.
I'll just quote a portion of HallsofIvy's excellent post:And how do you know that it is irrational?
In [itex]x^3+ x^2- 1= 0[/itex] the leading coeffient is 1 and the constant term is -1 which has, as integer factors, only 1 and -1 so the only "possible" rational roots are 1 and -1 and it is easy to see that they do not satisfy the equiation. Therefore, [itex]x^3+ x^2- 1[/itex] cannot be factored with integer or rational coefficients.