Hi, I have two questions that I can't solve:

Q1) Given that X - P is a factor of the expression X^2 - (P + 2)X - P^2 + 4P + 8, calculate the possible values of P

A1) -2, 4

My Attempt:

Let X^2 - (P+2)X - P^2 + 4P + 8 by f(x)

f(P) = 0

(P)^2 - (P+2)(P) - P^2 + 4P + 8 = 0

P^2 - P^2 - 2P - P^2 + 4P + 8 = 0

-2P + 4P + 8 = 0

2P = -8

P = -4

I have no ideal why I keep getting -4 instead of two numbers

Q2) A cubic equation f(x) = 0 has roots -3, -1 and 4. f(x) leaves a remainder of 12 when it is divided by x+2. Find the remainder when f(x) is divided by x^2-2x-1.

A2) -16x - 20

My Attempt:

(X+3)(X+1)(X-4) = 12

(X+3)(X^2-3X-4) = 12

X^3-3X^2-4X+3X^2-9X-12 = 12

X^3 -13X-12 = 12

X^3-13X-24 = 0

Division:

X^3-13X-24 = 0 / x^2-2x-1 = -8x-22

Any help is appreciate, thanks

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