If `f(x)` is a polynomial of degree `<3,` then, `f(x)/((x−a)(x−b)(x−c))​`is equals to

If f(x) be a polynomial of degree 1, then Delta^2f(x) = __________(fill in the blanks)

If int(tan^(9)x)dx=f(x)+log|cosx|, where f(x) is a polynomial of degree n in tan x, then the value of n is

If g(x)=(f(x))/((x-a)(x-b)(x-c)) ,where f(x) is a polynomial of degree <3 , then intg(x)dx=|[1,a,f(a)log|x-a|],[1,b,f(b)log|x-b|],[1,c,f(c)log|x-c|]|-:|[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|+k (dg(x))/(dx)=|[1,a,-f(a)(x-a)^(-2)],[1,b,-f(b)(x-b)^(-2)],[1,c,-f(c)(x-c)^(-2)]|:-|[1,a,a^2],[1,b,b^2],[1,c,c^2]|

If a^2+b^2+c^2=-2a n df(x)= |[1+a^2x,(1+b^2)x,(1+c^2)x],[(1+a^2)x,1+b^2x,(1+c^2)x],[(1+a^2)x,(1+b^2)x,1+c^2x]| , then f(x) is a polynomial of degree 0 b. 1 c. 2 d. 3

Let f(x) be the polynomial of degree n, then Delta^(n-1) f(x) is a polynomial of degree.

If a^(2)+b^(2)+c^(2)=-2 and f(x)=|(1+a^(2)x,(1+b^(2))x,(1+c^(2))x),((1+a^(2))x,1+b^(2)x,(1+c^(2))x),((1+a^(2))x,(1+b^(2))x,1+c^(2)x)| then f(x) is a polynomial of degree-

f(x) is a polynomial of degree 4 with real coefficients such that f(x)=0 is satisfied by x=1,2,3 only then f'(1).f'(2).f'(3) is equal to :

f(x) is a polynomial of degree 3 passing through the origin having local extrema at x=+-2 Statement 1 : Ratio of areas in which f(x) cuts the circle x^2+y^2=36i s1: 1. Statement 2 : Both y=f(x) and the circle are symmetric about the origin.

If n be an odd negative integer, then prove that (x + 1) is a polynomial of degree (x^(n)+1) .