Divide `4p ^(2) + 2p +2` by '2p' and write division fact.

Divide p(x) by g(x) and find the quotient and remainder : p(x)=x^(4)-5x+6, g(x)=2-x^(2)

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

If p is a natural number, then prove that p^(n+1) + (p+1)^(2n-1) is divisible by p^(2) + p +1 for every positive integer n.

Devide p(x) by g(x) in each of the following cases and verify division algorithm: p(x)= x^(2)+4x+4, g(x)= x+2

Write ( p + 2q + r) ^(2) in expanded from.

Find the remainder when x ^(3) - px ^(2) + 6x -p is divided by x -p.

Let P and Q be 3 xx3 matrices with P != Q . If P^(3) = Q^(3) and P^(2) Q = P^(2)Q = Q^(2) P , then determinant of (P^(2) + Q^(2)) is equal to :

If p=-2 find the value of : 4p+7

(i) Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: p(x)=x^3-3x^2+5x-3,g(x)=x^2-2 (ii) 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 (iii) Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: p(x)=x^4-5x+6,g(x)=2-x^2