the polynomial 2x^3 + px^2 +qx +r is divisible by x^2-1, but when divided by x-3 it has remainder 8. what is (p-r).q

Question

anonymous · Answer

a)10 b)-10 c)20 d)-20

anonymous · Answer

the first statement tells you two things
if you replace $x$ by 1 you get 0
and if you replace $x$ by -1 you also get 0
last statement says if you replace $x$ by 3 you get 8

anonymous · Answer

yes, i know.

anonymous · Answer

so unless there is some snappier way to do this, you have to solve the system of equations 
$$2+p+q+r=0$$
$$-2+p-q+r=0$$
$$54p+9p+3q+r=8$$

anonymous · Answer

check my arithmetic, 
first one i replaced x by 1
second one i replaces x by -1 and third one i replaced x by 3

anonymous · Answer

okay, thank you, i didnt know that i had to use systems of equations! i'll do that then! :)

anonymous · Answer

we can also write 
$$p+q+r=-2$$
$$p-q+r=2$$
$$9p+3q+r=-46$$

anonymous · Answer

i had a typo on the last one
i put a p where there should not have been one

anonymous · Answer

its okay :) i'll try work it out later