A. Long division
Multiply y+7 by y to get y^2+7y. Subtract product
(y^2+9y+9) - (y^2+7y) = 2y+9
Now multiply y+7 by 2 to get 2y+14. Subtract product
Remainder = (2y+9)-(2y+14) = -5
B. using the Polynomial Remainder Theorem
which says that if a polynomial f(y) is divided by a linear expression (x-a), the remainder equals f(a).
Here f(y)=y^2+9y+9, and (x-a)=(x-(-7)), i.e. a=-7
according to the Polynomial Remainder Theorem,
Remainder = f(-7) = (-7)^2+9(-7)+9=49-63+9 = -5 (as before)
