Suppose $a$ and $b$ are real numbers such that the polynomial $x^3+ax^2+bx+15$ has a factor of $x^2-2$. Find the value of $a^2b^2$.
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Tags: algebra, polynomial
Suppose $a$ and $b$ are real numbers such that the polynomial $x^3+ax^2+bx+15$ has a factor of $x^2-2$. Find the value of $a^2b^2$.