Draw the graphs of $y = x^3$.
| x | -2 | -1 | 0 | 1 | 2 |
| y | -8 | -1 | 0 | 1 | 8 |
Therefore, the zeros of the cubic polynomials $x^3$ are:
$x^3 =0$ i.e $x=0$
Note that 0 is the only zero of the polynomial $x^3$.
Also 0 is the x-coordinate of the only point where the graph of $ y = x^3$ intersects the x-axis.
Consider the cubic polynomials $x^3 - x^2$.
Draw the graphs of $y = x^3 - x^2$.
| x | -2 | -1 | 0 | 1 | 2 |
| y | -12 | -2 | 0 | 0 | 4 |
Let $y= x^3 - x^2$ and equate them to zero.
$x^3 - x^2 =x^2(x-1)$ i.e $x=0$ and $x =1$
Similarly, 0 and 1 are the only zeroes of the polynomial $x^3 - x^2$.
Also,these values are the x-coordinates of the only points where the graph of $y =x^3 - x^2$ intersects the x-axis.