# How do you find the zeros and use a sign chart to sketch the polynomial #F(x)=x^3(x+2)^2#?

##### 1 Answer

Determination of the zeros and a sign chart of

#### Explanation:

**Finding the zeros of #f(x)=x^3(x+2)^2#**

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

are

and the only unique factors are

Therefore

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.