Question

aratati ca pentru orice x apartine n valoarea expresiei x^3+2x^2-4x-8 supra x2+4x+4 ,este un numar intreg

Answer 1

x³+2x²-4x-8/x²+4x+4=x²(x+2)-4(x+2)/(x+2)²=(x+2)(x²-4)/(x+2)²=

=(x+2)(x+2)(x-2)/(x+2)²=(x+2)²(x-2)/(x+2)²=x-2∈Z