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.
-Crosses the $x$-axis at $- 3,0$, and 1 ; lies above the $x$-axis between $- 3$ and 0 ; lies below the $x$-axis between 0 and $1 .$
A) $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 3 x$
B) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 3 x$
C) $f ( x ) = - x ^ { 3 } - 2 x ^ { 2 } + 3 x$
D) $f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 3 x$

Question

Quizplus · Accepted Answer

The zeros of the polynomial $f(x) = x^3 + 2x^2 - 3x$ are $x = -3, 0, 1$, which can be found by factoring the polynomial as $x(x+3)(x-1)$. Each zero has a multiplicity of 1, indicating the graph crosses the x-axis at each zero. The behavior of the graph between the zeros matches the description given.

Find the Zeros for the Polynomial Function and Give the Multiplicity