(x² + 5x + 6) ÷ (x + 2 )?

...........x+3 answer//
.........---------------
...x+2|x^2+5x+6
.........-(x^2+2x)
........-----------------
...............3x+6
.............-(3x+6)
..............----------
...................0

another method is:

..x^2+5x+6
=----------------
.......x+2

..(x+2)(x+3)
=--------------- x+2 is cancel
.......x+2)

=x+3 answer//

= (x² + 5x + 6)/(x + 2)
= ([x + 2][x + 3])/(x + 2)
= x + 3

Answer: x + 3

Checking back to the dividend, x² + 5x + 6:
= (x + 3)(x + 2)
= x(x) + x(2) + 3(x) + 3(2)
= x² + 2x + 3x + 6
= x² + 5x + 6

(x^2 + 5x + 6)/(x + 2)
= (x^2 + 3x + 2x + 6)/(x + 2)
= [(x^2 + 3x) + (2x + 6)]/(x + 2)
= [x(x + 3) + 2(x + 3)]/(x + 2)
= [(x + 3)(x + 2)]/(x + 2)
= x + 3

(x² + 5x +6)
-------------------- =
(x + 2)

(x+2) (x+3)
----------------- =
(x + 2)

cancel (x + 2)....

(x + 3)

(x+2)(x+3)/ x+2


x+3 x+2 's cancel out

x+3

(x^2 + 5x + 6) / (x + 2 )
= [(x + 2)(x + 3)] / (x + 2)
= x + 3

x+3