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

p is a prime number and n

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

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

If p is a fixed positive integer, prove by induction that p^(n +1) + (p + 1)^(2n - 1) is divisible by P^2+ p +1 for all n in N .

For the three events A ,B ,a n dC ,P (exactly one of the events AorB occurs) =P (exactly one of the two evens BorC ) =P (exactly one of the events CorA occurs) =pa n dP (all the three events occur simultaneously) =p^2w h e r e 0 < p < 1//2. Then the probability of at least one of the three events A ,Ba n dC occurring is a. (3p+2p^2)/2 b. (p+3p^2)/4 c. (p+3p^2)/2 d. (3p+2p^2)/4

if the roots of the quadratic equation (4p - p^(2) - 5)x^(2) -(2p−1)x+3p=0 are greater then - 2 less then 4 then p lie in the interval