The Quotient Has a Remainder Too
Difficulty: Hard · Topics: Algebra, Polynomials, Remainder Theorem
Bo‘linmaning ham qoldig‘i bor
When P(x) is divided by x-2, the quotient is Q(x) and the remainder is -1. When Q(x) is divided by x+1, the remainder is 4.
Let R(x) be the remainder when P(x) is divided by (x-2)(x+1). Find R(3).
P(x) ni x-2 ga bo‘lganda bo‘linma Q(x), qoldiq -1 bo‘ladi. Q(x) ni x+1 ga bo‘lganda qoldiq 4 bo‘ladi.
R(x) — P(x) ni (x-2)(x+1) ga bo‘lgandagi qoldiq bo‘lsin. R(3) ni toping.