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.
-$$f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 33 x + 36$$
A) $- 3$, multiplicity 2 , touches the $x$-axis and turns around;
$- 4$, multiplicity 1 , crosses the $x$-axis.
B) 3 , multiplicity 1 , crosses the $x$-axis;
$- 3$, multiplicity 1 , crosses the $x$-axis;
$- 4$, multiplicity 1 , crosses the $x$-axis.
C) 3 , multiplicity 1 , crosses the $x$-axis;
$- 3$, multiplicity 2 , touches the $x$-axis and turns around;
$- 4$, multiplicity 1 , crosses the $x$-axis.
D) $- 3$, multiplicity 2 , crosses the $x$-axis;
$- 4$, multiplicity 1 , touches the $x$-axis and turns around

Question

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.
-$$f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 33 x + 36$$
A) $- 3$, multiplicity 2 , touches the $x$-axis and turns around; 
$- 4$, multiplicity 1 , crosses the $x$-axis.
B) 3 , multiplicity 1 , crosses the $x$-axis;
$- 3$, multiplicity 1 , crosses the $x$-axis;
$- 4$, multiplicity 1 , crosses the $x$-axis.
C) 3 , multiplicity 1 , crosses the $x$-axis;
$- 3$, multiplicity 2 , touches the $x$-axis and turns around; 
$- 4$, multiplicity 1 , crosses the $x$-axis.
D) $- 3$, multiplicity 2 , crosses the $x$-axis;
$- 4$, multiplicity 1 , touches the $x$-axis and turns around

Quizplus · Accepted Answer

The polynomial can be factored as $(x + 3)^2(x + 4)$. The zero $-3$ has multiplicity 2, so the graph touches the x-axis and turns around. The zero $-4$ has multiplicity 1, so the graph crosses the x-axis.

Find the Zeros for the Polynomial Function and Give the Multiplicity