Question

Cần gấp ạ

Answer 1

Bài 2:

a: \(\frac{A}{B}=\frac{8x^2-4x+1}{2x+1}\)

\(=\frac{8x^2+4x-8x-4+5}{2x+1}=\frac{4x\left(2x+1\right)-4\left(2x+1\right)+5}{2x+1}\)

\(=4x-4+\frac{5}{2x+1}\)

Để A chia hết cho B thì 5⋮2x+1

=>2x+1∈{1;-1;5;-5}

=>2x∈{0;-2;4;-6}

=>x∈{0;-1;2;-3}

b: \(\frac{A}{B}=\frac{2x^3-3x^2+2x+2}{x^2+1}\)

\(=\frac{2x^3+2x-3x^2-3+5}{x^2+1}=\frac{2x\left(x^2+1\right)-3\left(x^2+1\right)+5}{x^2+1}\)

\(=2x-3+\frac{5}{x^2+1}\)

Để A chia hết cho B thì 5⋮\(x^2+1\)

mà \(x^2+1\ge1\forall x\)

nên \(x^2+1\in\left\lbrace1;5\right\rbrace\)

=>\(x^2\in\left\lbrace0;4\right\rbrace\)

=>x∈{0;2;-2}

c: \(\frac{A}{B}=\frac{12x^3-7x^2-14x+14}{4x-5}\)

\(=\frac{12x^3-15x^2+8x^2-10x-4x+5+9}{4x-5}\)

\(=\frac{3x^2\left(4x-5\right)+2x\left(4x-5\right)-\left(4x-5\right)+9}{4x-5}=3x^2+2x-1+\frac{9}{4x-5}\)

Để A chia hết cho B thì 9⋮4x-5

=>4x-5∈{1;-1;3;-3;9;-9}

=>4x∈{6;4;8;2;14;-4}

=>x∈{3/2;1;2;1/2;7/2;-1}

mà x nguyên

nên x∈{1;2;-1}