Consider the two univariate polynomials p(x) = x^3 − 12x^2 + 41x − 42; and q(x) = x^2 − 2x − 35

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Lets Take q(x) = x^2 -2x -35.

To find its root we equate it with zero

x^2 - 2x - 35 = 0

Factorizing;

x^2 - 7x + 5x - 35 = 0

x(x - 7) + 5(x - 7) = 0

(x-7)(x+5) = 0

x = 7 or x = -5

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p(7) = q(7) = 0; x-7 is the root

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