Simplify the following:
(x+3) (x^3-7 x+6)
The possible rational roots of x^3-7 x+6 are x = ±1, x = ±2, x = ±3, x = ±6. Of these, x = 1, x = 2 and x = -3 are roots. This gives x-1, x-2 and x+3 as all factors:
(x-2) (x-1) (x+3) (x+3)
Combine powers. (x+3) (x-1) (x-2) (x+3) = (x-2) (x-1) (x+3)^(1+1):
(x-2) (x-1) (x+3)^(1+1)
1+1 = 2:
Answer: |(x-2) (x-1) (x+3)^2 =x^4 + 3x^3 - 7x^2 - 15x + 18
