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Finding the Value of an Expression

Let a>0,and l...

Question

Let a>0,and let P(x) be a polynomial with integer coefficients such that P(1)=P(3)=P(5)=P(7)=a , and P(2)=P(4)=P(6)=P(8)=-a. The smallest possible value of a =5× Q. what is Q

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P (x) = x^{6} + a x^{5} + b x^{4} + c x^{3} + d x^{2} + e x + f

P (1) = 1; P (2) = 2; P (3) = 3; P (4) = 4; P (5) = 5

P (6) = 6

P (7)

P (1) = 1

P (2) = 2

P (3) = 3

P (4) = 5

P (6)

P (x)

4

P (1) = 2, P (2) = 5, P (3) = 10

P (4) = 17

P (5) =

P (x) = x^{4} + a x^{3} + b x^{2} + c x + d

P (1) = 1, P (2) = 8, P (3) = 27, P (4) = 64

P (5)

5

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