Hi everybody!! Can smb help me to factorize an expression,pleaseeee?

I need to factorize this three-variable expression:

-2766624 - 62500*cos(x)*h^2 + 716000*R^2*cos(x) + 2454124*cos(x)^2 + 15625*cos(x)^2*h^4 + 272750*cos(x)^2*h^2*R^2 + 187500*cos(x)^3*h^2 + 1049656*R^4*cos(x)^2 + 375000*cos(x)^3*R^2+562500*cos(x)^4 + 140625*cos(x)^4*R^4

Answer 1

[Walter Roberson]

It does not factor. You can collect similar cos(x)^N terms and you can do some factorization of the result:

-2766624 + 140625*(2-2*R+R^2)*(2+2*R+R^2)*cos(x)^4 + (187500*(h^2+2*R^2))*cos(x)^3 + (2454124+15625*h^4+272750*R^2*h^2+1049656*R^4)*cos(x)^2 + (500*(-125*h^2+1432*R^2))*cos(x)

[Aizhan Merey]

<It does not factor.> it means that the expression is not equal 0?!

[Aizhan Merey]

and is it possible to define cos(x) by R,h?

[Walter Roberson]

"factorize" means to express an expression as two or more terms multiplied together. If you _are_ able to factor an expression, then you can find the zeros of the expression by solving for the zeros of the individual terms, which is usually a much easier problem. If, though, you are not able to factor an expression, just means that you are not able to factor the expression and does not mean that you cannot solve the expression for zeros.

If you examine your expression, you will see that the only time x occurs, it is in the context of cos(x). To solve for cos(x), you can do a simple change of variables, such as substituting T for cos(x). The result is a quartic (polynomial in 4th degree.) Collect the powers of T. You can then read off the powers of T to construct a roots() call that you can use for numeric R and h.

[Walter Roberson]

Remember, though, that any solutions for T that are themselves complex, or which are real but abs(T) > 1, imply values of x that are complex, since cos(x) over real values is always in the range -1 to 1.

Answer 2

[Aizhan Merey]

:DD,, Waaaaw! understood xDD.. thaaaaaaanks!!!!!