#### Answer

$$x^3-x^2+x-15$$

#### Work Step by Step

In order to add or subtract polynomials, we combine like terms. Like terms must (1) be raised to the same power and (2) consist of the same variable (i.e. x and y are not like terms). It is also important to note that numbers are all like terms with each other when not multiplied by anything. Thus, combining like terms, we obtain:
$$ x^3-3x-7-x^2+4x-8\\ x^3-x^2+x-15$$