Factorise the expression and divide them as directed. (y^2 + 7y + 10) ÷ (y + 5)

A. y - 2
B. y + 1
C. y + 2
D. y - 1

We are given the expression:

(y^2 + 7y + 10) ÷ (y + 5)

Step 1: Factorising the numerator
We need to factorise the quadratic expression y^2 + 7y + 10. To factorise it, we look for two numbers that multiply to give 10 (the constant term) and add up to 7 (the coefficient of y).

The two numbers are 2 and 5 because: 2 * 5 = 10 2 + 5 = 7

So, we can factorise the expression as: y^2 + 7y + 10 = (y + 2)(y + 5)

Step 2: Simplifying the expression
Now the expression becomes: ((y + 2)(y + 5)) ÷ (y + 5)

We can cancel the common factor of (y + 5) in the numerator and the denominator: = (y + 2)

Step 3: Conclusion
The simplified expression is (y + 2).

Thus, the correct answer is: C. y + 2