The polynomial remainder theorem states that the remainder upon dividing a polynomial [tex]p(x)[/tex] by [tex]x-c[/tex] is the same as the value of [tex]p(c)[/tex], so to find [tex]p(-10)[/tex] you need to find the remainder upon dividing
[tex]\dfrac{2x^3+14x^2-58x}{x+10}[/tex]
You have
..... | 2 ... 14 ... -58
-10 | ... -20 ... 60
--------------------------
..... | 2 ... -6 .... 2
So the quotient and remainder upon dividing is
[tex]\dfrac{2x^3+14x^2-58x}{x+10}=2x-6+\dfrac2{x+10}[/tex]
with a remainder of 2, which means [tex]p(-10)=2[/tex].
