Question

How do you find the remainder when `(x^3 - 5x^2 + 7x +3) ÷ (x-2)`?

Answer 1

You could use either polynomial long division or synthetic division to get Remainder `= 29`

Explanation:

synthetic division

`{: (,"|",1,-5,+7,color(white)("x")+3), (,"|",,+2,+6,+26), ("-----",,"----","----","----","-----"), (xx (+2),"|",1,-3,+13,color(white)("X")color(red)(29)) :}`

polynomial long division

`{: (,,x^2,-3x,+13,), (,,"-----","-----","-----","-----"), (x-2,")",x^3,-5x^2,+7x,+3), (,,x^2,-2x^2,,), (,,"----","-----",,), (,,,3x^2,+7x,), (,,,3x^2,-6x,), (,,,"-----","----",), (,,,,13x,+3), (,,,,13x,-26), (,,,,"-----","-----"), (,,,,,color(red)(29)) :}`

If you need details of the process for either of these methods, please ask as a separate question.