a: A chia hết cho B
=>\(2x^3-x^2-x+3⋮2x-3\)
=>\(2x^3-3x^2+2x^2-3x+2x-3+6⋮2x-3\)
=>\(2x-3\inƯ\left(6\right)\)
=>\(2x-3\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)
=>\(2x\in\left\{4;2;5;1;6;0;9;-3\right\}\)
=>\(x\in\left\{2;1;\dfrac{5}{2};\dfrac{1}{2};3;0;\dfrac{9}{2};-\dfrac{3}{2}\right\}\)
mà x nguyên
nên \(x\in\left\{0;1;2;3\right\}\)
b: C chia hết cho D
=>\(3x^4-5x^3+7x^2-9x+2⋮3x+1\)
=>\(3x^4+x^3-6x^3-2x^2+9x^2+3x-12x-4+6⋮3x+1\)
=>\(6⋮3x+1\)
=>\(3x+1\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)
=>\(3x\in\left\{0;-2;1;-3;2;-4;5;-7\right\}\)
=>\(x\in\left\{0;-\dfrac{2}{3};\dfrac{1}{3};-1;\dfrac{2}{3};-\dfrac{4}{3};\dfrac{5}{3};-\dfrac{7}{3}\right\}\)
mà x nguyên
nên \(x\in\left\{0;-1\right\}\)
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