How do you find the zeros and use a sign chart to sketch the polynomial #F(x)=x^3(x+2)^2#?
Determination of the zeros and a sign chart of
Finding the zeros of
Remember that a function has the value zero at (and only at) points where some factor of the function has the value zero.
The factors of
and the only unique factors are
For non-zero values of
We can pick arbitrary values within each interval to determine if
Unfortunately this does not** tell us any detailed information about the behavior of
Just for reference, here is what the graph should look like, but you would need to use something beyond the zeros and a sign chart to sketch this.