Question

How do you divide `(3x^4+22x^3+ 15 x^2+6x+8)/(x-4)`?

Answer 1

Use synthetic division or polynomial long division to get
`3x^3+34x^2+151x+610` with remainder `2448`

Explanation:

synthetic division
`{: (,,3,22,color(white)("X")15,color(white)("X")6,color(white)("XX")8), (,,,12,136,604,2440), (,,"----","----","----","----","----"), (xx(+4),"|",color(blue)(3),color(blue)(34),color(blue)(151),color(blue)(610),color(red)(2448)) :}`

polynomial long division
`{: (,,3x^3,+34x^2,+15x,+610,), (,,"----","-------","-------","-------","-------"), (x-4,")",3x^4,+22x^3,+15x^2,6x,+8), (,,3x^4,-12x^3,,,), (,,"----","-------",,,), (,,,34x^3,+15x^2,,), (,,,34x^3,-136x^2,,), (,,,"-------","-------",,), (,,,,151x^2,+6x,), (,,,,151x^2,-604x,), (,,,,"-------","-------",), (,,,,,610x,+8), (,,,,,610x,-2440), (,,,,,"-------","-------"), (,,,,,,2448) :}`