Divide `p^4+p^3-p^2+1` by `p-1`

Divide 4p^(3)-4p^(2)+6p-(5)/(2) by 2p-1 using factorisation method.

Divide as directed: 4(3p+1)(2p+5) -:(3p +1)

Divide as directed: -(p+1)(p+2)(p+3) -:p(p+1) .

If p(x) is divided by (x+1), the remainder got is given by [p(1/2), p(-1/2), p(-1), p(1)] .

Theorem 1.3 : Let p be a prime number. If p divides a^2 , then p divides a, where a is a positive integer.

If p(x) is divided by (2x-1),the remainder got is given by [p(1/2), p(-1/2), p(-2), p(2)] .

When (p^(2)-p-29) is divided by (p-6) the remainder is 1.

Factorize the expressions and divide them as directed : (p^2+5p+ 4) ÷ (p+1).