Question

How do you divide `(4x^2 + 2x -5)/(x +3)`?

Answer 1

Either use polynomial long division or synthetic division to get:
`4x-10` with remainder `25`

Explanation:

Synthetic division
#{: (,,4,2,-5), (,,,-12,30), (,,"----","----","----"), (xx(-3),"|",color(blue)(4),color(blue)(- 10),color(red)(25)) :}#

Polynomial long division
#{: (,,color(blue)(4x),color(blue)(-10),), (,,"----","----","----"), (x+3,")",4x^2,+2x,-5), (,,4x^2,+12x,), (,,"----","----",), (,,,-10x,-5), (,,,-10x,-30), (,,,"----","----"), (,,,,color(red)(25)) :}#