How can factorise a polynomial with complex roots, without showing their numerical values of the roots, but only their symbolical value.

For example I have:

factor(x^4 - x^2 + x - 1)

and it shows me the following factorisation: (x-1)(x^3+x^2+1) but I want to also factorise x^3+x^2+1 but the roots should be displayed symbolically without numerical values of these roots. Then how to implement this task?

In the book I am reading it's stated to use factor(x^4-x^2+x-1, I), but it doesn't seem to be working.

How do I find with maple's help  for which parameter m does the equation:

x^2+2*m*x-6*x=m^3 have one of its roots equal to the square of the other root?

Thanks!

I have the following equations which I want to plot the curves of them by maple's:

1. |x+2|+|y|=3

2. |y|-|x|=2.

How to implement this task in maple?

thanks!

I have some algebraic expression which I want to expand.

I used the ExpandSteps command to show me the steps, but I guess I used it incorrectly.

Attached below the file with the commands.

It should be expanded to -\Delta*\sin^2(\theta), but I want maple to show me the steps.

ExpandSteps.mw
 

Download ExpandSteps.mw

I have the following question, plot the graph of mu=5*log_10(D_L/10) where D_L=(c/H_0)*\int_0^z dz'/[A(1+z')^4+B(1+z)^3+C]^{1/2} with resepct to z, where A,B,C are numerical values given beforehand, and c is the speed of light and H_0 is the current Hubble constant.

Can someone please help with this simple plotting assignment.

Thanks, just by experience, can I learnt these syntax languages.

Peace out!