a: Ta có: f(x):g(x)

\(=\dfrac{3x-a}{x-1}\)

\(=\dfrac{3x-3+3-a}{x-1}\)

\(=3+\dfrac{3-a}{x-1}\)

Để f(x):g(x) có số dư là 2 thì 3-a=2

hay a=1

b: Ta có: f(x):g(x)

\(=\dfrac{x^3-2x^2+3x+a}{x+1}\)

\(=\dfrac{x^3+x^2-3x^2-3x+6x+6+a-6}{x+1}\)

\(=x^2-3x+6+\dfrac{a-6}{x+1}\)

Để f(x):g(x) là phép chia hết thì a-6=0

hay a=6

a: Thay a=3 vào f(x), ta được:

\(f\left(x\right)=x^3-2x^2+3x+3\)

\(\dfrac{f\left(x\right)}{g\left(x\right)}=\dfrac{x^3-2x^2+3x+3}{x+1}\)

\(=\dfrac{x^3+x^2-3x^2-3x+6x+6-3}{x+1}\)

\(=x^2-3x+6-\dfrac{3}{x+1}\)

a: Thay a=2 vào f(x), ta được:

f(x)=3x-2

f(x):g(x)

\(=\dfrac{3x-2}{x-1}\)

\(=\dfrac{3x-3+1}{x-1}\)

\(=3+\dfrac{1}{x-1}\)

`f(x):g(x)` dư 2

`=>f(x)-2\vdots g(x)`

`=>x-3x+5x-a-2\vdots x-1`

`=>3x-3+a+1\vdots x-1`

`=>3(x-1)+a+1\vdots x-1`

`=>a+1=0=>a=-1`

a: Ta có: f(x):g(x)

\(=\dfrac{3x-a}{x-1}\)

\(=\dfrac{3x-3+3-a}{x-1}\)

\(=3+\dfrac{3-a}{x-1}\)

Để f(x):g(x) có số dư là 2 thì 3-a=2

hay a=1

`a)f(x):g(x)` dư 2

`=>f(x)-2\vdots g(x)`

`=>x^3-3x^2+5x-a-2\vdots  x-1`

`=>x^3-x^2-2x^2+2x+3x-3-a+1\vdots  x-1`

`=>x^2(x-1)-2x(x-1)+3(x-1)-a+1\vdots  x-1`

`=>(x-1)(x^2-2x+3)-a+1\vdots  x-1`

Mà `(x-1)(x^2-2x+3)\vdots x-1`

`=>-a+1=0=>a=1`

Ta có: f(x):g(x)

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

\(=\dfrac{x^3-x^2-2x^2+2x+3x-3-a+3}{x-1}\)

\(=x^2-2x+3+\dfrac{-a+3}{x-1}\)

Để f(x):g(x) có số dư là 2 thì 3-a=2

hay a=1

d: Ta có: f(x):g(x)

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

\(=\dfrac{x^3+x^2-3x^2-3x+6x+6-1}{x+1}\)

\(=x^2-3x+6+\dfrac{-1}{x+1}\)

Để f(x) chia hết cho g(x) thì \(x+1\in\left\{1;-1\right\}\)

hay \(x\in\left\{0;-2\right\}\)

f(1)=0

=>5+a-5-a²=0

=>a(1-a)=0

=>a=0 hoặc a=1