Question

Answer 1

Ta có \(\left(x^3-4x^2+5x-1\right):\left(x-3\right)\)

\(=\left(x^3-3x^2-x^2+3x+2x-6+5\right):\left(x-3\right)\\ =\left[x^2\left(x-3\right)-x\left(x-3\right)+2\left(x-3\right)+5\right]:\left(x-3\right)\\ =x^2-x+2\left(\text{dư }5\right)\)

Phép chia hết xảy ra \(\Leftrightarrow5⋮\left(x-3\right)\Leftrightarrow x-3\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\)

\(\Leftrightarrow x\in\left\{-2;2;4;8\right\}\)

Answer 2

\(\Leftrightarrow x-3\in\left\{1;-1;5;-5\right\}\)

hay \(x\in\left\{4;2;8;-2\right\}\)