Factor Theorem - the polynomial P(x) has x – r as a factor if and only if P(r) = 0

Use the Remainder Theorem to find the remainder R in each of the following.
〖(x^4-x〗^3+2) ÷ (x+2)
〖(x^3-2x〗^2+x+6) ÷ (x-3)
〖(x^4-3x〗^3+〖4x〗^2-6x+4) ÷ (x-2)

Use the Factor Theorem to determine whether or not the first polynomial is a factor of the second. Then, give the remainder if the second polynomial is divided by the first polynomial.

x-1 ; 〖 x〗^2+2x+5
x-1 ; 〖 x〗^3-x-2
x-4 ; 〖 〖2x〗^3-9x〗^2+9x-20

Factor the following
〖 (x〗^2+5x+6)
〖 x〗^2-9