Does x^3 + x^2 -1 factor? and if yes.... how?
There is actually an algorithmic way to find the roots for polynomials with degree less than five.Which method would you use?
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.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.
You should know the remainder and factor theorem.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.
I didn't learn the iterative method until I was in college, but I don't know if that's typical.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.