Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
-$$f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 20 x + 16$$
A) $- 2$, touches the $x$-axis and turns around;
$- 4$, crosses the $x$-axis.
B) $- 2$, crosses the $x$-axis;
$- 4$, touches the $x$-axis and turns around
C) 2 , crosses the $x$-axis;
$- 2$, crosses the $x$-axis;
$- 4$, crosses the $x$-axis.
D) 2, crosses the x-axis;
$- 2$, touches the $x$-axis and turns around;
$- 4$, crosses the $x$-axis.

Question

Quizplus · Accepted Answer

The given polynomial can be factored as $f(x) = (x + 2)^2 (x + 4)$. The x-intercepts are at $x = -2$ and $x = -4$. At $x = -2$, the factor is squared, indicating the graph touches the x-axis and turns around. At $x = -4$, the factor is not squared, indicating the graph crosses the x-axis.

Find the X-Intercepts of the Polynomial Function f(x)=x3+8x2+20x+16f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 20 x + 16f(x)=x3+8x2+20x+16

Find the X-Intercepts of the Polynomial Function $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 20 x + 16$