How to factor completely?

Question

 

How to factor 3x^4+3x^3-3x-3

Answer 1

3x⁴ = 3x³ · x
3x³ = 3x³ · 1
a³ - b³ = (a - b)(a² + ab + b²)
~~~~~~~~~ 
3x⁴ + 3x³ - 3x -3 =
(3x⁴ + 3x³) - (3x + 3) =
3x³(x +1) - 3(x + 1) =
(x +1)(3x³ - 3) =
3(x +1)(x³ - 1) =
3(x + 1)(x - 1)(x² + x + 1)

Answer 2

Hey Daisy!

Looks like x= 1, -1 both work => (x+1)(x-1)= (x^2-1) can come out & bring 3 out:

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

(x^4-x^2) <<<<<<<<<<<<\/     \/   \/

0+x^3+x^2                                 \/    \/

   (x^3-x)<<<<<<<<<<<<<<<<\/    \/

   0+x^2-1 <<<<<<<<<<<<<<<<<<\/

Answer ==> 3(x^2+x+1)(x+1)(x-1) ... I like getting started by trying x= 1,-1, etc ... Best wishes