Remainder Theorem

Question

1)2x^2+6x+3 will have the same remainder when divided by x+p and x-2q. p does not equal to -2q. So what is p-2q?
Answer

Remainder Theorem for you is : if f(x) a polynomial is divided by a linear divisor x-a the remainder is f(a)

So f(x) 2x^2+6x + 3
x+p = x-(-p)
f(-p) = 2(-p)^2 -6p + 3
=2p^2 -6p + 3

f(2q) = 2(2q)^2 + 6.2q + 3
= 8q^2 + 12q + 3

now it seems they have the same remainder so : 2p^2 -6p + 3 =8p^2 +12q +3
2p^2-8q^2 -6p -12q = 0
2(p^2 -4q^) -6(p + 2q) = 0
or 2(p-2q)(p+2q) -6(p + 2q) =0
or (p+2q)(2(p-2q) - 6) =0
so 2(p-2q) -6 =0
or p-2q =6/2
or p-2q =3