Question

How do you evaluate `\frac { x ^ { 2} + 3x + 22} { x + 5}`?

Answer 1

`(x^2+3x+22)/(x+5)=color(green)((x-2) R:32)`

Explanation:

Method 1: Synthetic Division
#{: (,,x^2,x^1,x^0), (,"|",1,3,22), (underline" + ",,underline(color(white)(0)),underline(-5),underline(10)), (color(blue)(-(+5)),"|",1,-2,color(red)(32)), (,,x^1,x^0,R) :}#

Method 2: Long Division
`color(white)("XXX")underline(color(white)("X")xcolor(white)("X")-2color(white)("XX")`
`x+5 )x^2+3x+22`
`color(white)("XXxX")underline(x^2+5x)`
`color(white)("XXXXXX")-2x+22`
`color(white)("XXXXXX")underline(-2x-10)`
`color(white)("XXXXXXXXXX")32`