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D( x )
2*x+5 = 0
2*x+5 = 0
2*x+5 = 0
2*x+5 = 0 // - 5
2*x = -5 // : 2
x = -5/2
x in (-oo:-5/2) U (-5/2:+oo)
(2*x^3+17*x^2+38*x+15)/(2*x+5) = 0
2*x^3+17*x^2+38*x+15 = 0
2*x^3+17*x^2+38*x+15 = 0
{ 1, -1, 3, -3, 5, -5, 15, -15 }
1
x = 1
2*x^3+17*x^2+38*x+15 = 72
1
-1
x = -1
2*x^3+17*x^2+38*x+15 = -8
-1
3
x = 3
2*x^3+17*x^2+38*x+15 = 336
3
-3
x = -3
2*x^3+17*x^2+38*x+15 = 0
-3
x+3
2*x^2+11*x+5
2*x^3+17*x^2+38*x+15
x+3
-2*x^3-6*x^2
11*x^2+38*x+15
-11*x^2-33*x
5*x+15
-5*x-15
0
2*x^2+11*x+5 = 0
DELTA = 11^2-(2*4*5)
DELTA = 81
DELTA > 0
x = (81^(1/2)-11)/(2*2) or x = (-81^(1/2)-11)/(2*2)
x = -1/2 or x = -5
x in { -5, -1/2, -3}
(x+5)*(x+1/2)*(x+3) = 0
((x+5)*(x+1/2)*(x+3))/(2*x+5) = 0
( x+1/2 )
x+1/2 = 0 // - 1/2
x = -1/2
( x+3 )
x+3 = 0 // - 3
x = -3
( x+5 )
x+5 = 0 // - 5
x = -5
x in { -1/2, -3, -5 }
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