If the expression y² + 10y + 24 has a factor of (y + 4), what is another factor of the expression y² + 10y + 24?

To find another factor of the expression y² + 10y + 24, we can start by using the given information that one of the factors is (y + 4).

We can perform polynomial division to divide y² + 10y + 24 by (y + 4). Here’s how it works:

1. Set up the division:

       y + 4 | y² + 10y + 24

2. Determine what you need to multiply (y + 4) by to get the first term of the dividend:
3. Multiply y by (y + 4) to get y² + 4y.
4. Subtract this result from (y² + 10y + 24):

       y + 4 | y² + 10y + 24
                  - (y² + 4y)
                 __________________
                       6y + 24

3. Next, we have 6y + 24. Now, repeat the process:
4. Determine what you need to multiply (y + 4) by to match the first term of 6y:
5. You’ll multiply (6) by (y + 4): that gives you 6y + 24.
6. Subtract this from (6y + 24):

       y + 4 | y² + 10y + 24
                  - (y² + 4y)
                 __________________
                       6y + 24
                      - (6y + 24)
                 __________________
                             0

Since the remainder is 0, that means the division has been done correctly. Thus, the full factorization of the expression y² + 10y + 24 can be written as:

   (y + 4)(y + 6) = y² + 10y + 24

From this, we conclude that another factor of y² + 10y + 24 is (y + 6).

In summary, the factors of the expression y² + 10y + 24 are (y + 4) and (y + 6).