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D( x )
x-5 = 0
x-5 = 0
x-5 = 0
x-5 = 0 // + 5
x = 5
x in (-oo:5) U (5:+oo)
(x^3-(4*x^2)-(47*x)+210)/(x-5) = 0
(x^3-4*x^2-47*x+210)/(x-5) = 0
x^3-4*x^2-47*x+210 = 0
x^3-4*x^2-47*x+210 = 0
{ 1, -1, 2, -2, 3, -3, 5, -5, 6, -6, 7, -7, 10, -10, 14, -14, 15, -15, 21, -21, 30, -30, 35, -35, 42, -42, 70, -70, 105, -105, 210, -210 }
1
x = 1
x^3-4*x^2-47*x+210 = 160
1
-1
x = -1
x^3-4*x^2-47*x+210 = 252
-1
2
x = 2
x^3-4*x^2-47*x+210 = 108
2
-2
x = -2
x^3-4*x^2-47*x+210 = 280
-2
3
x = 3
x^3-4*x^2-47*x+210 = 60
3
-3
x = -3
x^3-4*x^2-47*x+210 = 288
-3
5
x = 5
x^3-4*x^2-47*x+210 = 0
5
x-5
x^2+x-42
x^3-4*x^2-47*x+210
x-5
5*x^2-x^3
x^2-47*x+210
5*x-x^2
210-42*x
42*x-210
0
x^2+x-42 = 0
DELTA = 1^2-(-42*1*4)
DELTA = 169
DELTA > 0
x = (169^(1/2)-1)/(1*2) or x = (-169^(1/2)-1)/(1*2)
x = 6 or x = -7
x in { -7, 6, 5}
(x+7)*(x-6)*(x-5) = 0
(x+7)*(x-6) = 0
( x+7 )
x+7 = 0 // - 7
x = -7
( x-6 )
x-6 = 0 // + 6
x = 6
x in { -7, 6 }
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