<PRE><B>Question 994806</B>
Root x=4 of multiplicity 2 means that P(x) has a factor (x-4)^2
Roots of multiplicity 1 at x=0 means P(x) has a factor x and at
x=-3 means a factor (x+3) 
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P(x) = x * (x-4)^2 * (x+3)
P(x) = (x^2+3x) * (x-4)^2
P(x) = (x^2+3x) * (x^2 -8x +16)
P(x) = x^4 -5x^3 -8x^2 +48x
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now we use point (5,32)
32 = 5^4 -5(5^3) -8(5^2) +48(5)
32 = 625 -625 -200 +240
to make this work we have to subtract 8 from the right side of =, therefore
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P(x) = x^4 -5x^3 -8x^2 +48x -8 and then
32 = 32
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