Answer:
-5
Step-by-step explanation:
The leading term in a polynomial consist on the highest degree term. To get the highest degree term, we need to reorder the polynomial from left to right, starting with the highest degree term.
In this case:
[tex]f(x)=\frac{1}{2} x^{2} +8-5x^{3} -19x[/tex]
reordering
[tex]f(x)=-5x^{3} +\frac{1}{2}x^{2} -19x+8[/tex]
So, the leading coefficient is the one with the leading term:
[tex]-5x^{3}[/tex]
So, it is -5
