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.
-$$f ( x ) = 3 ( x + 1 ) ( x + 7 ) ^ { 2 }$$
A) $- 1$, multiplicity 1 , crosses $x$-axis; $- 7$, multiplicity 2 , touches $x$-axis and turns around
B) 1 , multiplicity 1 , crosses $x$-axis; 7 , multiplicity 2 , touches $x$-axis and turns around
C) $- 1$, multiplicity 1 , touches $x$-axis and turns around; $- 7$, multiplicity 2 , crosses $x$-axis
D) 1 , multiplicity 1 , touches $x$-axis and turns around; 7 , multiplicity 2 , crosses $x$-axis

Question

Quizplus · Accepted Answer

The zeros of the polynomial are found by setting each factor equal to zero: $x + 1 = 0$ gives $x = -1$ with multiplicity 1, indicating the graph crosses the x-axis at this point. $x + 7 = 0$ gives $x = -7$ with multiplicity 2, indicating the graph touches the x-axis and turns around at this point.

Find the Zeros for the Polynomial Function and Give the Multiplicity