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

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

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=

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

(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