Answer:
x² + 13x + 50 + [tex]\frac{57}{x-5}[/tex]
Step-by-step explanation:
Using Synthetic division
divisor is (x - 5) , thus evaluate at h = 5
5 | 1 8 - 25 - 193
5 65 250
-----------------------------
1 13 50 57 ← remainder = 57
The coefficients of the quotient are 1, 13, 50 , that is
x² + 13x + 50
Thus
[tex]\frac{x^3+8x^2-25x-193}{x-5}[/tex] = x² + 13x + 50 + [tex]\frac{57}{x-5}[/tex]
