- fa 2+60) (42-45) 9. If x= 522 PAC +24=(x+4). 91%) then find value of p

$$\begin{gathered} x^3-5x^2-px+24=(x+4)·q\left(x\right) \\ Thus, x^3-5x^2-px+24 is divided by \\ x+4 and produces quotient q\left(x\right). \\ x+4\sqrt{x^3-5x^2-px+24}(x^2-9x+6 \\ {x}^3+4x^2 \\ \overline{-9x^2-px} \\ -9x^2\pm 36x \\ \overline{\left(36-p\right)x+24} \\ 6x+24 \\ \overline{0} \\ Thus 36-p=6 \\ \mathit{p}\mathbf{=}\mathbf{36}\mathbf{-}\mathbf{6}\mathbf{=}\mathbf{30} \end{gathered}$$