Answer: See below
Step-by-step explanation:
To find the factor,
f(x) = 0
[tex]\begin{aligned}&2 x^{4}-72 x^{2}=0 \\&2 x^{2}\left(x^{2}-36\right)=0 \\&x^{2}\left(x^{2}-36\right)=0 \\&x \times x \times(x-6) \times(x+6)=0 \\&\mathrm{x}=0,0,6,-6\end{aligned}[/tex]
So,
x = 0 multiplicity 2
x = -6 multiplicity 1
x = 6 multiplicity 1
For an even multiplicty, the graph touches the x-axis, and for an odd multiplicty, the graph crosses the x-axis
Therefore,
x = 0 multiplicty 2, Touch
x = -6 multiplicty 1, Cross
x = 6 multiplicty 1, Cross
