Question

What is the quotient when `2x^3 + x + 3` is divided by x + 1?

Answer 1

`(2x^3+x+3)div(x+1) = color(blue)(2x^2-2x+3)`
`color(white)("XXXXXXXX")` with a `color(green)("R")`emainder `= color(green)(0)`

Explanation:

Using synthetic division:
`(2x^3+x+3) div (xcolor(red)(+)1)`

`{: (,,color(brown)(x^3),color(white)("X")color(brown)(x^2),color(white)("X")color(brown)(x^1),color(white)("X")color(brown)(x^0)), (,"|",2,color(white)("X")0,color(white)("X")1,color(white)("X")3), (,"|",,-2,+2,-3), (bar(color(white)("XXX")),,bar(color(white)("XXX")),bar(color(white)("XXX")),bar(color(white)("XXX")),bar(color(white)("XXX"))), (xx (color(red)(-)1),"|",color(blue)(2),color(blue)(-2),color(white)("X")color(blue)(3),color(white)("X")color(green)(0)), (,,color(brown)(x^2),color(white)("X")color(brown)(x^1),color(white)("X")color(brown)(x^0), color(white)("X")color(green)(R)) :}`