Box "polynomials at proper points" (cancelling)

Sometimes we have a limit of a rational function (ratio of polynomials) at a proper point that turns out to be "zero over zero". While usually the l'Hospital rule should handle it, sometimes it is easier to simply cancel. Note that if a polynomial p satisfies p(a) = 0, then the factor (x − a) can be factored out of the polynomial. If both the numerator and the denominator of a rational function are zero at a, then consequently the factor (x − a) can be factored.

Example:

Cancelling can be sometimes done also for other ratios. One such example is this problem in Solved Problems, there is also one example in the box "difference of roots" and one in the box "indeterminate ratio".

Next box: difference of roots
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