Give an example of polynomials `f(x),\ \ g(x),\ \ q(x)` and `r(x)` satisfying `f(x)=g(x)dotq(x)+r(x)` , where degree `r(x)=0` .

Give examples of polynomials p(x), g(x), 9(x) and r(x), which satisfy the division algorithm and deg r(x)=0

Give examples of polynomials p(x), g(x), 9(x) and r(x), which satisfy the division algorithm and deg q(x)= deg r(x)

Assertion : 3x^(2)+x-1=(x+1)(3x-2)+1 . Reason : If p(x) and g(x) are two polynomials such that degree of p(x)ge degree of g(x) and g(x)ge0 then we can find polynomials q(x) and r(x) such that p(x)=g(x).q(x)+r(x) , where r(x)=0 or degree of r(x)lt degree of g(x) .

On dividing a polynomial p(x) by a non-zero polynomial q(x) , let g(x) be the quotient and r(x) be the remainder then = q(x)* g(x) + r(x), where

If a real polynomial of degree n satisfies the relation f(x)=f(x)f''(x)"for all "x in R" Then "f"R to R

On dividing the polynomial f(x)=x^(3)-3x^(2)+x+2 by a polynomial g(x), the quotient q(x) and remainder r(x) where q(x)=x-2 and r(x)=-2x+4 respectively.Find the polynomial g(x) .

If f(x) g(x) and h(x) are three polynomials of degree 2 and Delta = |( f(x), g(x), h(x)), (f'(x), g'(x), h'(x)), (f''(x), g''(x), h''(x))| then Delta(x) is a polynomial of degree (dashes denote the differentiation).

Let g(x) be a polynomial of degree one and f(x) be defined by f(x)=-{g(x),x 0 If f(x) is continuous satisfying f'(1)=f(-1) then g(x) is

Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g(x),x 0} Find g(x) such that f(x) is continuous and f'(1)=f(-1)