Determine the zeros and the multiplicity of any multiple zeros.
y = x² (x+1)²(2x+3)
The zeros are when y is zero. So you can set x equal to 0, -1, and -3/2 (or -1.5) to make y=0. Those are the x-intercepts and the zeros.
The Multiplicity is the degree at which each separate part is. For x=0, the multiplicity is two because the first x that would make y=0 has a power of two.
For the second part, (x+1)², the multiplicity is again the power so it would be two.
For the final part since there is no power we can assume it is a one.
Sorry for the late response. Hope it still helps you.