Question

Answer 1

`a)A=B.Q+R`

`<=>2x^3-x^2-x+1=(x^2-2x)Q+R`

`<=>2x^3-4x^2+3x^2-6x+5x+1=(x^2-2x)Q+R`

`<=>2x(x^2-2x)+3(x^2-2x)+5x+1=(x^2-2x)Q+R`

`<=>(x^2-2x)(2x+3)+5x+1=(x^2-2x)Q+R`

  `=>{(Q=2x+3),(R=5x+1):}`

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`b)A=B.Q+R`

`<=>5x^3-x+2=(x^2+2x-3)Q+R`

`<=>5x^3+10x^2-15x-10x^2-20x+30+34x-28=(x^2+2x-3)Q+R`

`<=>5x(x^2+2x-3)-10(x^2+2x-3)+34x-28=(x^2+2x-3)Q+R`

`<=>(x^2+2x-3)(5x-10)+34x-28=(x^2+2x-3)Q+R`

    `=>{(Q=5x-10),(R=34-28):}`