For this case we must find the quotient of [tex]x ^ 2 + 11x + 24[/tex] between [tex]x + 4[/tex]
As you can see in the figure, we must build a quotient in such a way that when multiplied by the divisor, we eliminate the terms of the dividend until we reach the remainder.
Answer:
Quotient: x + 7
Remainder: -4
See attached image