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.
-$$f ( x ) = 3 ( x - 2 ) ( x + 3 ) ^ { 3 }$$
A) $- 2$, multiplicity 1 , crosses $x$-axis; 3 , multiplicity 3 , crosses $x$-axis
B) 2, multiplicity 1 , crosses $x$-axis; $- 3$, multiplicity 3 , crosses $x$-axis
C) $- 2$, multiplicity 1 , touches $x$-axis; 3 , multiplicity 3 , touches $x$-axis and turns around
D) 2 , multiplicity 1 , crosses $x$-axis; $- 3$, multiplicity 3 , touches $x$-axis and turns around

Question

Quizplus · Accepted Answer

The zeros of the polynomial are found by setting $f(x) = 0$. The given polynomial $f(x) = 3(x - 2)(x + 3)^3$ has zeros at $x = 2$ and $x = -3$. The zero at $x = 2$ has a multiplicity of 1, which means the graph crosses the x-axis at this point. The zero at $x = -3$ has a multiplicity of 3, which is odd, so the graph also crosses the x-axis at this point.

Find the Zeros for the Polynomial Function and Give the Multiplicity