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Dividing a Polynomial by a Polynomial

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Question

Find the zeroes of the polynomial $p (x) = x^{3} - 13 x^{2} + 32 x - 60$ , if it is given that the product of its two zeroes is $10$ .

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Solution

$\begin{matrix} x^{2} - 7 x - 10 x^{2} - 5 x - 2 x - 10 A = (x - 5) B = (x - 2) C = (x - 6) \end{matrix}$

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