$$y = (x+h)^3(x-h)^2(x-k)(x+k)$$

The equation above is graphed in the $xy$-plane. If $h$ and $k$ are positive constants and $h \neq k$, how many distinct $x$-intercepts does the graph have?

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The $x$-intercepts are the values that cause any of the binomial factors to equal 0.

$$(x+h)=0$$ $$(x-h)=0$$ $$(x-k)=0$$ $$(x+k)=0$$ $$x = -h, h, k, \text{ and } -k$$

Because $h \neq k$ and the values are positive (not zero), we get $\boxed{4}$ distinct solutions. The exponents change the multiplicity of the factor, but does not affect the value.