Here, dividend is
[tex]f(x)=x^3-x^2-17x-15[/tex]
Divisor is (x-5).
Let the quotient be Q(x) and teh remainder be R(x).
By the divison algorithm,
[tex]x^3-x^2-17x-15=(x-5)Q(x)+R(x)[/tex]
Now,
[tex]\begin{gathered} f(5)=125-25-85-15 \\ =0 \end{gathered}[/tex]
Therefore, there is no remainder by the division algorithm.
Quotient is
[tex]x^2+4x+3[/tex]
