Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each zero.
-$$f ( x ) = - 2 ( x - 4 ) ( x + 5 ) ^ { 3 }$$
A) 4 , multiplicity 1 , crosses $x$-axis; $- 5$, multiplicity 3 , crosses $x$-axis
B) $- 4$, multiplicity 1 , crosses $x$-axis; 5 , multiplicity 3 , crosses $x$-axis
C) 4 , multiplicity 1 , touches the $x$-axis and turns around; $- 5$, multiplicity 3 , touches $x$-axis and turns around
D) - 4 , multiplicity 1 , touches the $x$-axis and turns around; 5 , multiplicity 3 , touches $x$-axis and turns around

Question

Quizplus · Accepted Answer

The zeros of the polynomial are $x = 4$ with multiplicity 1, which means the graph crosses the $x$-axis at $x = 4$, and $x = -5$ with multiplicity 3, which is odd, so the graph also crosses the $x$-axis at $x = -5$.

Find the Zeros for the Polynomial Function and Give the Multiplicity