(5s^3+5s^2+90)/(s+3)

Solution for (5s^3+5s^2+90)/(s+3) equation:

D( s )

s+3 = 0

s+3 = 0

s+3 = 0

s+3 = 0 // - 3

s = -3

s in (-oo:-3) U (-3:+oo)

(5*s^3+5*s^2+90)/(s+3) = 0

5*s^3+5*s^2+90 = 0

5*(s^3+s^2+18) = 0

s^3+s^2+18 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18 }

1

s = 1

s^3+s^2+18 = 20

1

-1

s = -1

s^3+s^2+18 = 18

-1

2

s = 2

s^3+s^2+18 = 30

2

-2

s = -2

s^3+s^2+18 = 14

-2

3

s = 3

s^3+s^2+18 = 54

3

-3

s = -3

s^3+s^2+18 = 0

-3

s+3

s^2-2*s+6

s^3+s^2+18

s+3

-s^3-3*s^2

18-2*s^2

2*s^2+6*s

6*s+18

-6*s-18

0

s^2-2*s+6 = 0

DELTA = (-2)^2-(1*4*6)

DELTA = -20

DELTA < 0

s in { -3} 

5*(s+3) = 0

5 = 0

s belongs to the empty set