Question

find the remainder when x3-x2+3x+6 is divided by x+3

Answer 1

$p(x) = x {}^{3} - x {}^{2} + 3x + 6 \\ g(x) = x + 3 \\ by \: remainder \: theorem \\ x + 3 = 0 \\ x = \: - 3 \\ so \: remainder \: = p( - 3) \\ p( - 3) = ( - 3) {}^{3 } - ( - 3) {}^{2} + 3 \times - 2 + 6 \\ = - 27 - 9 - 6 + 6 \\ = - 33$

Answer 2

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