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Long Division Method to Divide Two Polynomials

Divide: 3x3+2...

Question

Divide: $(3 x^{3} + 2 x^{2} - 1) b y (x + 2)$

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Solution

$3 x^{3} + 2 x^{2} - 1 = 3 x^{2} (x + 2) - 6 x^{2} + 2 x^{2} - 1 = 3 x^{2} (x + 2) - 4 x^{2} - 1 = 3 x^{2} (x + 2) - 4 x^{2} - 8 x + 8 x - 1 = 3 x^{2} (x + 2) - 4 x (x + 2) + 8 x - 1 = 3 x^{2} (x + 2) - 4 x (x + 2) + 8 x + 16 - 16 - 1 = 3 x^{2} (x + 2) - 4 x (x + 2) + 8 (x + 2) - 16 - 1 = 3 x^{2} (x + 2) - 4 x (x + 2) + 8 (x + 2) - 17 = (x + 2) (3 x^{2} - 4 x + 8) - 17$
Quotient and Reminder are = $3 x^{2} - 4 x + 8$ and -17 respectively.

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