Answer:
[tex]x+4[/tex]
Step-by-step explanation:
This question is essentially asking: [tex]p(x)^2*(x-3)=x^3+5x^2-8x-48[/tex]. Find [tex]p(x)[/tex].
The left hand side can be factored into [tex](x-3)(x+4)^2[/tex] by the rational root theorem and polynomial division.
We can then divide both sides of the equation to get [tex]p(x)^2=(x+4)^2[/tex].
Finally, we take the square root of both sides to obtain [tex]p(x)=x+4[/tex].
So, the answer is [tex]\boxed{x+4}[/tex]
