When a polynomial is dived by x - a, to find the remainder, we can plug is x = a into the equation and find the remainder.
When it is divided by x + a, the remainder is found by plugging in x = -a.
Now, the polynomial here is:
[tex]x^2+15x+9[/tex]It is divided by x + 5, so we need to plug in x = -5 to get the remainder, which is:
[tex]\begin{gathered} x^2+15x+9 \\ (-5)^2+15(-5)_{}+9 \\ =-41 \end{gathered}[/tex]The remainder is - 41, 1st answer choice.
