The expression y² + 10y + 24 has a factor of y + 4. What is another factor of y² + 10y + 24?

To find another factor of the quadratic expression y² + 10y + 24, we can start by using the factor we already know, which is y + 4.

Using polynomial division, we can divide y² + 10y + 24 by y + 4.

1. Set up the long division:
2. Divide the leading term y² by the leading term y to get y.
3. Multiply y by y + 4 to get y² + 4y.
4. Subtract y² + 4y from y² + 10y + 24 to get 6y + 24.
5. Now divide 6y by y to get 6.
6. Multiply 6 by y + 4 to get 6y + 24.
7. Subtract to find the remainder, which is 0.

Since the division yields no remainder, we conclude that:

y² + 10y + 24 = (y + 4)(y + 6)

Thus, another factor of the expression y² + 10y + 24 is y + 6.