Polynomials: zeros, multiplicity, and whether the graph crosses through the $x$ axis there Here are the choices: A) -3, multiplicity 1, touches x-axis; 3, multiplicity 3 B) -3, multiplicity 1, crosses x-axis; 3, multiplicity 3, crosses x-axis C) 3, multiplicity 1, crosses x-axis; -3, multiplicity 3, crosses x-axis D) 3, multiplicity 1, touches x-axis; -3, multiplicity 3 The function is $$f(x) = 5(x+3)(x-3)^3.$$ Please help me figure this out. And if possible can you provide the steps and explanation :)

Hint: In $(x-a)^m(x-b)^n$, $x=a$ is a zero of multiplicity $m$ and $x=b$ is a zero of multiplicity $n$.

When the multiplicity of a root is even, the graph does NOT cross through the $x$ axis at that point, but it does when the multiplicty is odd.