Question

How do you divide #(2x^3+15x+12) /(x+1) # using polynomial long division?

Answer 1

`2x^2-2x+17-5/(x+1)` with remainder `(-5)`
(see Explanation for polynomial long division)

Explanation:

#{: (,,color(blue)(2x^2),color(blue)(-2x),color(blue)(+17),), (,,"----","------","------","-----"), (x+1,")",2x^3,,+15x,+12), (,,2x^3,+2x^2,,), (,,"----","------",,), (,,,-2x^2,+15x,), (,,,-2x^2,color(white)("X")-2x,), (,,,"------","-------",), (,,,,color(white)("X")17x,color(white)("X")12), (,,,,color(white)("X")17x,+17), (,,,,"-------","------"), (,,,,,color(red)(-5)) :}#