Answer to Question #160931 in Calculus for Alondra aban

Question

Your friend Eliza asks your help in drawing rough sketch of the graph of

𝑃(𝑥) = −(𝑥 − 1)(𝑥 + 3)2 by means of the Leading Coefficient Test. How will you 

explain the behavior of the graph?

Answer 1

$\textsf{Leading term:} \,\,-x^3 \\ \textsf{Leading coefficient:} \,\,-1.\\ \textsf{Because the degree is odd}\\ \textsf{and the leading coefficient is}\\ \textsf{negative, the graph rises to the}\\ \textsf{left and falls to the right as}\\ \textsf{shown in the figure.}$