A Linear and a Quadratic Remainder
Difficulty: Hard · Topics: Algebra, Polynomials, Remainder Theorem
Chiziqli va kvadrat qoldiq
f(x) leaves remainder 4 when divided by x-1, and remainder 2x-1 when divided by x^2+1.
Let R(x) be the remainder when f(x) is divided by (x-1)(x^2+1). Find R(3).
f(x) ni x-1 ga bo‘lganda 4 qoldiq, x^2+1 ga bo‘lganda 2x-1 qoldiq qoladi.
R(x) — f(x) ni (x-1)(x^2+1) ga bo‘lgandagi qoldiq bo‘lsin. R(3) ni toping.