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Just look at the graph of a function.

If a polynomial P(x) has a squared factor such as (x - c)^2, then x = c is a double root of P(x) = 0. In this case, the graph of y = P(x) is tangent to the x-axis at x = c.

If a polynomial P(x) has a cubic factor such as (x - c)^3, then x = c is a triple root of

P(x) = 0. In this case, the graph of y = P(x) flattens out around (c, 0), and crosses the x-axis at this point.

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