Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where $(p x) = x^{3} - 6 x^{2} + 9 x + 3, g (x) = x - 1$

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Solution

$(p x) = x^{3} - 6 x^{2} + 9 x + 3 g (x) = x - 1 R e m a i n d e r = p (1) p (1) = (1)^{3} - 6 (1)^{2} + 9 (1) + 3 = 1 - 6 + 9 + 3 = 7 R e m a i n d e r = 7$

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p (x) = x^{3} - 2 x^{2} - 4 x - 1

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p (x) = 4 x^{3} - 12 x^{2} + 14 x - 3, g (x) = 2 x - 1

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