Question

How do you divide `(4x ^ { 2} - x - 1) \div ( x + 2)`?

Answer 1

`4x-9" Remainder: "17`

Explanation:

By synthetic division
Noting that `(x+2)=0` if `x=color(red)(-2)`
#{: (,,,x^2,x^1,x^0), (,," | ",4,-1,-1), (underline(color(white)("XX")),underline(color(white)("XX")),underline(" | "),underline(color(white)("X")),underline(-8),underline(+18)), (color(red)(-2),xx," | ",4,-9,+17), (,,,x^1,x^0,R) :}#

By long division

`color(white)("XXX")underline(color(white)("x")4xcolor(white)("x")-9color(white)("XXXX"))`
`x+2 ) 4x^2color(white)("x")-xcolor(white)("x")-1`
`color(white)("XXxX")underline(4x^2color(white)("x")+8x)`
`color(white)("XXXXxXX")-9x`
`color(white)("XXXxXXX")underline(-9xcolor(white)("x")-18)`
`color(white)("XXXXXXXXXXX")+17`