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

The equation (a(x-b)(x-c))/((a-b)(a-c)) + (b(x-c)(x-a))/((b-c)(b-a))+ (c (x-a) (x-b))/((c-a)(c-b))= x is satisfied by

The equation (a(x-b)(x-c))/((a-b)(a-c)) + (b(x-c)(x-a))/((b-c)(b-a))+ (c (x-a) (x-b))/((c-a)(c-b))= x is satisfied by

Statement-1: If a, b, c are distinct real numbers, then a((x-b)(x-c))/((a-b)(a-c))+b((x-c)(x-a))/((b-c)(b-a))+c((x-a)(x-b))/((c-a)(c-b))=x for each real x. Statement-2: If a, b, c in R such that ax^(2) + bx + c = 0 for three distinct real values of x, then a = b = c = 0 i.e. ax^(2) + bx + c = 0 for all x in R .

Statement-1: If a, b, c are distinct real numbers, then a((x-b)(x-c))/((a-b)(a-c))+b((x-c)(x-a))/((b-c)(b-a))+c((x-a)(x-b))/((c-a)(c-b))=x for each real x. Statement-2: If a, b, c in R such that ax^(2) + bx + c = 0 for three distinct real values of x, then a = b = c = 0 i.e. ax^(2) + bx + c = 0 for all x in R .

Simplify: ((x^(a))/(x^(-b)))^(a-b)xx((x^(b))/(x^(-c)))^(b-c)xx((x^(c))/(x^(-a)))^(c-a)

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