Find factor

Question

 Find factor
x3-1/x3+4

Answer 1

(x³ - 1)/(x³+4)

 

Let's recall the following rules for factoring cubics.

 

a³ - b³ = (a-b)(a² + ab + b²)

a³ + b³ = (a+b)(a² - ab + b²)

 

With these in mind, let first factor the numerator

x³ - 1 = (x-1)(x²+x+1)

 

and the denominator

x³ + 4 = (x+2)(x²-2x+4)

 

(x-1) (x²+x+1)

(x+2)(x²-2x+4)

 

Hope this helps.