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[" If "(x^(4))/((x-a)(x-b)(x-c))=p(x)+(A...

[" If "(x^(4))/((x-a)(x-b)(x-c))=p(x)+(A)/(x-a)+(B)/(x-b)+(c)/(x-c)" then "],[p(x)=]

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If (x^(3))/((x-a)(x-b)(x-c))=1 +(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then A=

If (x^(3))/((x-a)(x-b)(x-c))=1 +(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then A=

(x^(3))/((x-a)(x-b)(x-c))=1+(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then A=

(x^(4))/((x-a)(x-b)(x-c))=P(x)+(A)/(x-a)+(B)/(x-b)+(C)/(x-c)rArr P(x)=

(a^2/(x-a)+b^2/(x-b)+c^2/(x-c)+a+b+c)/(a/(x-a)+b/(x-b)+c/(x-c))

Let P(x)=((x-a)(x-b))/((c-a)(c-b))c^(2)+((x-b)(x-c))/((a-b)(a-c))a^(2)+((x-c)(x-a))/((b-c)(b-a))b^(2) Prove that P(x) has the property that P(y)=y^(2) for all y in R .

Suppose, a, b, c are three distinct real numbers. Let P (x) = ((x-b)(x-c))/((a-b)(a-c))+((x-c)(x-a))/((b-c)(b-a))+((x-a)(x-b))/((c-a)(c-b)) . When simplified, P (x) becomes