Final answer:
To solve for m and n in the given equation, we expand the right side and equate the coefficients of like terms to obtain two equations. By solving these equations, we find that m = 10 and n = 6.
Step-by-step explanation:
To solve for m and n in the equation y^2 + my + 24 = (y + 4)(y + n), we need to expand the right side of the equation and equate it to the left side. This will give us two equations:
y^2 + my + 24 = y^2 + (4 + n)y + 4n
We can then equate the coefficients of like terms to solve for m and n. From the y terms, we have m = 4 + n. From the constant terms, we have 24 = 4n. Solving for n gives us n = 6, and substituting this value in the first equation gives us m = 10. Therefore, m = 10 and n = 6.