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D( x )
x+3 = 0
x+3 = 0
x+3 = 0
x+3 = 0 // - 3
x = -3
x in (-oo:-3) U (-3:+oo)
(12*x^3+31*x^2-(17*x)-6)/(x+3) = 0
(12*x^3+31*x^2-17*x-6)/(x+3) = 0
12*x^3+31*x^2-17*x-6 = 0
12*x^3+31*x^2-17*x-6 = 0
{ 1, -1, 2, -2, 3, -3, 6, -6 }
1
x = 1
12*x^3+31*x^2-17*x-6 = 20
1
-1
x = -1
12*x^3+31*x^2-17*x-6 = 30
-1
2
x = 2
12*x^3+31*x^2-17*x-6 = 180
2
-2
x = -2
12*x^3+31*x^2-17*x-6 = 56
-2
3
x = 3
12*x^3+31*x^2-17*x-6 = 546
3
-3
x = -3
12*x^3+31*x^2-17*x-6 = 0
-3
x+3
12*x^2-5*x-2
12*x^3+31*x^2-17*x-6
x+3
-12*x^3-36*x^2
-5*x^2-17*x-6
5*x^2+15*x
-2*x-6
2*x+6
0
12*x^2-5*x-2 = 0
DELTA = (-5)^2-(-2*4*12)
DELTA = 121
DELTA > 0
x = (121^(1/2)+5)/(2*12) or x = (5-121^(1/2))/(2*12)
x = 2/3 or x = -1/4
x in { -1/4, 2/3, -3}
(x+1/4)*(x-2/3)*(x+3) = 0
(x+1/4)*(x-2/3) = 0
( x+1/4 )
x+1/4 = 0 // - 1/4
x = -1/4
( x-2/3 )
x-2/3 = 0 // + 2/3
x = 2/3
x in { -1/4, 2/3 }
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