" Find all cubic polynomials "p(x)" such that "(x-1)^(2)" is a factor of "p(x)+2" and "(x+1)^(2)" is a factor of "p(x)-2

Find all cubic polnomials p(x) such that (x-1)^(2) is a factor of p(x)+2 and (x+1)^(2) is a factor of p(x)-2 .

p(x)=(x+2)(x-3) + k ,(x-2) is a factor of p(x) :- p(x) Examine whether (x+1) is a factor of p(x).

p(x)=(x+2)(x-3) + k ,(x-2) is a factor of p(x):- Find k.

Find all polynomials p satisfying p(x+1)=p(x)+2x+1

For the polynomial p(x), if p(2) = 0, then ……… is a factor of p(x).

Find k if (x-1) is a factor of p(x)=2x^(2)+kx+sqrt(2)

If a is defined by f (x)=a_(0)x^(n)+a_(1)x^(n-2)+a_(2)x^(n-2)+...+a_(n-1)x+a_(n) where n is a non negative integer and a_(0),a_(1),a_(2),…….,a_(n) are real numbers and a_(0) ne 0, then f is called a polynomial function of degree n. For polynomials we can define the following theorem (i) Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and 'a' be a real number. if p(x) is divided by (x-a), then the remainder is equal to p(a). (ii) Factor theorem : Let p(x) be a polynomial of degree greater than or equal to 1 and 'a' be a real number such that p(a) = 0, then (x-a) is a factor of p(x). Conversely, if (x-a) is a factor of p(x). then p(a)=0. The factor of the polynomial x^(3)+3x^(2)+4x+12 is

Consider the polynomial p(x)= x^2-5x+6 :- Is (2x-1)a factor of p(x)? Why?

If p(x) be a polynomial such that p(-a/b)=0 , then one of the factor of p(x) is