A Square Divisor and a Linear One
Difficulty: Hard · Topics: Algebra, Polynomials, Remainder Theorem
Kvadrat bo‘luvchi va chiziqli bo‘luvchi
P(x) leaves remainder 2x+1 when divided by (x-1)^2, and remainder -6 when divided by x+2.
Let R(x) be the remainder when P(x) is divided by (x-1)^2(x+2). Find R(4).
P(x) ni (x-1)^2 ga bo‘lganda 2x+1 qoldiq, x+2 ga bo‘lganda -6 qoldiq qoladi.
R(x) — P(x) ni (x-1)^2(x+2) ga bo‘lgandagi qoldiq bo‘lsin. R(4) ni toping.