Question

divide
(y²+7y+10)÷(y+5)

Answer 1

first take
y^2 + 7y + 10

y^2 + 5y + 2y + 10 [by factorisation]

y (y + 5) + 2 (y + 5)

(y + 2)(y + 5) ... (1)

now
$\frac{ {y}^{2} + 7y + 10 }{(y + 5) } \\ \\ = \frac{(y + 5)(y + 2)}{(y + 5)} (from equation (1) \\ \\ ans. \: = (y + 2)$

Answer 2

            y + 2
        ---------------------
y + 5) y^2 + 7y + 10

          y^2 + 5y

          ----------------------

                     2y + 10

                     2y + 10

         -----------------------------

                          0.


Therefore the Quotient = y + 2. Remainder = 0.


Hope this helps!