Question: please refer to the picture above.

I think there is something wrong about my working as my remainder's answer is different from the choices, but i don't see anywhere went wrong. ="=

Mind helping me to check whether is there anything wrong in my working?

NOTE: I don't really know how to use [ math ] [ /math]. So, if you see some small p or big p, they're the same.

$\displaystyle

(x-1)(x+3)(-x+p)$

=($\displaystyle x^2$+2x-3)(-x+p)

=$\displaystyle -x^3$$\displaystyle +x^2$$\displaystyle p$$\displaystyle -2x^2$$\displaystyle +2xp+3x-3p$

let x be -4,

$\displaystyle -(-4)^3$ $\displaystyle + (-4)^2$$\displaystyle p$$\displaystyle -2(-4)^2$$\displaystyle + 2(-4)p +3(-4) -3p=10$

64 + 16p -32 -8p-12-3p=10

5p=-10

p=-2

let x be 4 and substitute p=-2,

-64 -32 -16 -16 +12 +6 =-110

my remainder is -110, but according to the choices, the remainder should be -126.