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

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

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

0 and 4 are the respective remainders when the polynomial p(x)=x^(3)-px+q is divided by (x - 2) and (x + 2). What will be the remainder when p(x) is divided by x ?

If x be a factor of the polynomial p(x) = (x - 1) (x - 2) (x - 3), then p(0) =

If p,q in N" satisfy the equation "x^(sqrtx) = (sqrtx)^(x) , then

Let P(x) and Q(x) be two polynomials. If f(x) = P(x^4) + xQ(x^4) is divisible by x^2 + 1 , then

If the polynomial p(x)=4x^(3)-px^(2)+x-q be divided by (x - 1) and (x + 2), the respective remainders are 0 and 3. Find the value of p and q.

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : p(x)=x^(4)-3x^(2)+4x+5,g(x)=x^(2)+1-x