Factorization and Simplifying.

[AstrophysicsX]

Homework Statement

Use Factorization to simplify the given expression.

Homework Equations

(x^3 + 3x^2 + 3x +1)/(x^4 + x^3 + x + 1)

The Attempt at a Solution

I can't get to the first step. I forgot how to factor exponents higher than x^2.

 

[LCKurtz]

Think about the binomial expansion of (a+b)³. Also you can check for roots using synthetic division. And remember a root x = r corresponds to a factor of x-r.

 

[stonecoldgen]

Theorem of the factor.

You can probably simplify the upper and the lower part, maybe even cancel out some stuff...

 

[AstrophysicsX]

But how to do that is the problem.

 

[Dick]

But how to do that is the problem.

If x=(-1) then the numerator and denominator are both 0. That means (x-(-1))=(x+1) is a common factor of the numerator and denominator. Now start factoring it out.

 

[NascentOxygen]

(x^3 + 3x^2 + 3x +1)/(x^4 + x^3 + x + 1)

I can't get to the first step. I forgot how to factor exponents higher than x^2.

As others have pointed out, x=-1 is a "solution" to the numerator (equaling zero). So this tells you that (x+1) is a factor of the numerator. So what is the other factor?

If you don't like doing division, you can solve by doing multiplication. To start with, let's look at just the numerator:

x³ + 3x² + 3x + 1 = (x+1)(x² + Mx + C)

Multiply the right hand side to remove the brackets, and equate the coefficients on each side to determine the values of the unknowns M and C.