Question

How do you use synthetic division to divide `(-3x^4)/(x+2)`?

Answer 1

`(-3x^4)/(x+2)=-3x^3+6x^2-12x+24` with a Remainder of `(-48)`

Explanation:

`(x+2)=0 rarr x=color(red)((-2))`
Synthetic division by `(x+2)` is equivalent to synthetic substitution with `x=color(red)((-2))`

#{:(,,color(grey)x^4,color(grey)x^3,color(white)("xx")color(grey)x^2,color(white)("x")color(grey)x^1,color(white)("xx")color(grey)x^0), (," | ",-3,0,color(white)("xx")0,color(white)("x")0,color(white)("xx")0), (ul(+color(white)("x"))," | ",ul(color(white)("Xx")),ul(6),ul(-12),ul(24),ul(-48)), (xxcolor(red)((-2))," | ",-3,6,-12,24,-48), (,,color(grey)(x^3),color(grey)(x^2),color(white)("x")color(grey)(x^1),color(grey)(x^0),color(grey)R) :}#