Problem:  Divide  
x2 + 5x + 9
x + 2


Set up the long division
x =   x2
x
.
Choose x since
x · x matches x2.
x2 + 2x = x(x + 2).
Subtract x2 + 2x from x2 + 5x + 9.
Result is 3x + 9.
3 =   3x
x
.
Choose 3 since
3 · x matches 3x.
3x + 6 = 3(x + 2).
Subtract 3x + 6 from 3x + 9.
Result is 3.
3 is the remainder.


Answer:   x2 + 5x + 9
x + 2
 =   x + 3 + 3
x + 2
.


Notes
x2 + 5x + 9 = (x + 2)(x + 3) + 3
Dividend x2 + 5x + 9
Divisor x + 2
Quotient x + 3
Remainder 3