Find the zeros of the given polynomial function and give the multiplicity of each. State whether the graph crosses or touches the x-axis at each zero. $f\left(x\right)=x^2\left(x-1\right)^3\left(2x+6\right)$

• A. Cross at $x=0,$ Cross at $x=1,$ Cross at $x=3$
• B. Touch at $x=0,$ Cross at $x=-1,$ Cross at $x=3$
• C. Cross at $x=0,$ Touch at $x=1,$ Touch at $x=-3$
• D. Touch at $x=0,$ Cross at $x=1,$ Cross at $x=-3$