`a.`
$\bullet\quad$ `f(x)+g(x)`
`(3x^2-x+1)+(x-1)`
`=3x^2-x+1+x-1`
`=3x^2-(x-x)+(1-1)`
`=3x^2-0+0`
`=3x^2`
$\bullet\quad$ `f(x)-g(x)`
`(3x^2-x+1)-(x-1)`
`=3x^2-x+1-x+1`
`=3x^2-(x+x)+(1+1)`
`=3x^2-2x+2`
$\bullet\quad$ `f(x) . g(x)`
`(3x^2-x+1)(x-1)`
`=3x^2(x-1)-x(x-1)+1(x-1)`
`=3x^3-3x^2-x^2+x+x-1`
`=3x^3-(3x^2+x^2)+(x+x)-1`
`=3x^3-4x^2+2x-1`
`b.`
Để `f(x) . g(x)+x^2 . [1-3 . g(x)]=5/2`
`(3x^2-x+1)(x-1)+x^2 . [1-3(x-1)]=5/2`
`<=>3x^2(x-1)-x(x-1)+1(x-1)+x^2 . [1-3(x-1)]=5/2`
`<=>3x^3-3x^2-x^2+x+x-1+x^2 . [1-3(x-1)]=5/2`
`<=>3x^3-(3x^2+x^2)+(x+x)-1+x^2 . [1-3(x-1)]=5/2`
`<=>3x^3-4x^2+2x-1+x^2 . [1-3(x-1)]=5/2`
`<=>3x^3-4x^2+2x-1+x^2 . (1-3x+3)=5/2`
`<=>3x^3-4x^2+2x-1+x^2 . (4-3x)=5/2`
`<=>3x^3-4x^2+2x-1+4x^2-3x^3=5/2`
`<=>(3x^3-3x^3)-(4x^2+4x^2)+2x-1=5/2`
`<=>0-0+2x-1=5/2`
`<=>2x-1=5/2`
`<=>2x=5/2+1`
`<=>2x=5/2+1/1`
`<=>2x=5/2+2/2`
`<=>2x=(5+2)/2`
`<=>2x=7/2`
`<=>x=7/2:2`
`<=>x=7/2:2/1`
`<=>x=7/2 . 1/2`
`<=>x=(7 . 1)/(2 . 2)`
`<=>x=7/4`
Vậy, `x=7/4` thì `f(x) . g(x)+x^2 . [1-3 . g(x)]=5/2.`
