Answer:
[tex]x^2+8x+12=(x+5)(x+3)-3.[/tex]
The quotient is [tex]x+3[/tex] and the remainder is -3.
Step-by-step explanation:
Dividing [tex]x^2+8x+12[/tex] by [tex]x+5,[/tex] multiply [tex]x+5[/tex] by x:
[tex](x+5)x=x^2+5x[/tex] and subtract it from [tex]x^2+8x+12:[/tex]
[tex]x^2+8x+12-(x^2+5x)=x^2+8x+12-x^2-5x=3x+12.[/tex]
Now multiply [tex]x+5[/tex] by 3:
[tex](x+5)\cdot 3=3x+15[/tex]
and subtract it from [tex]3x+12:[/tex]
[tex]3x+12-(3x+15)=3x+12-3x-15=-3.[/tex]
Thus,
[tex]x^2+8x+12=(x+5)(x+3)-3.[/tex]
The quotient is [tex]x+3[/tex] and the remainder is -3.
