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   giorgiana1976 Teacher
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   Due to the rule of division with reminder:

   P(x)=Q(x)*C(x)+R(x), where the degree of the polynomial

   R(x)<the degree of the polynomialQ(x). We've noticed that the degree of Q(x) is third degree, so the biggest degree of  R(x) is 2.

   R(x)=ax^2+bx+c

   The root of Q(x) are x1=1, x2=x3=-1.

   If we'll substitute x=1 in P(x), we'll obtain:

   P(1)= 1+2-5-10+2

   But P(x)=Q(x)*C(x)+R(x), P(1)=0*C(x) +a+b+c=a+b+c

   a+b+c=-10

   P(-1)=a-b+c

   P(-1)=1+2+5-10+2=0

   a-b+c=0, b=a+c

   But, we've noticed that x=-1 is a multiple root, so this one has to verify the first derivative ,too.

   P'(x)=2002x^2001+4000x^1999-25x^4-20x=-2a+b

   P'(-1)=-2002-4000-25+20=-6007

   -2a+b+a-b+c=-6007+0

   -a+c+a+b+c=-10-6007

   2c+b=-6017, b=-6017-2c, b=a+c

   a+c=-6017-2c,

   a=-6017-3c

   a+b+c=-10, -6017-3c-6017-2c+c=-10

   -4c=12034-10

   c=-12024/4, c=-3006

   b=-6017+6012, b=-5

   a=-6017+9018, a=3001

   R(x)=3001x^2-5x-3006

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   Posted by giorgiana1976 on Saturday May 30, 2009 at 1:17 PM