find the possible values of p, if (px-p) is divided by (x-4/p) and the remainder is p^2 -p
If a numerator N is divided by a denominator D, then the result will be a factor F along with a remainder R, such that,
N = D.F + R
We have,
Numerator N = px - p
Denominator D = x - 4/p
Remainder R = p^2 - p
Using N = D.F + R,
px - p = (x - 4/p) * F + p^2 - p
px = (x - 4/p) * F + p^2
p(x - p) = F.(x - 4/p)
This is an equation, which as such is true for all values of x.
By comparison of the coefficient of x and of the constant values, we get that F = p and p = 4/p => p = +/- 2
Answer: p has two possible values: p = +/- 2