# How do you use the leading coefficient test to determine the end behavior of the polynomial function #f(x)= -5(x2+1)(x-2)#?

##### 1 Answer

If the leading coefficient is negative, the polynomial function will eventually decrease to negative infinity; if the leading coefficient is positive, the polynomial function will eventually increase to positive infinity.

This answer assumes by leading coefficient you mean the coefficient of the highest powered

If

then if

For example if

Since the term with the highest exponent will eventually provide a value that exceeds the combined value of all other terms, the sign of that term determines the eventual direction of the function value.