How do you divide #(3x^4 + 2x^3  11x^2  2x + 5)/ (x^2  2) # using polynomial long division?
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To divide (3x^4 + 2x^3  11x^2  2x + 5) by (x^2  2) using polynomial long division, follow these steps:

Arrange the dividend and divisor in descending order of exponents. Dividend: 3x^4 + 2x^3  11x^2  2x + 5 Divisor: x^2  2

Divide the first term of the dividend by the first term of the divisor. (3x^4) / (x^2) = 3x^2

Multiply the divisor by the quotient obtained in step 2. 3x^2 * (x^2  2) = 3x^4  6x^2

Subtract the result obtained in step 3 from the dividend. (3x^4 + 2x^3  11x^2  2x + 5)  (3x^4  6x^2) = 2x^3  5x^2  2x + 5

Bring down the next term from the dividend. 2x^3  5x^2  2x + 5

Repeat steps 25 until all terms have been divided. (2x^3) / (x^2) = 2x 2x * (x^2  2) = 2x^3  4x
(2x^3  5x^2  2x + 5)  (2x^3  4x) = 5x^2 + 2x + 5
(5x^2) / (x^2) = 5 5 * (x^2  2) = 5x^2 + 10
(5x^2 + 2x + 5)  (5x^2 + 10) = 8

The quotient is the sum of the quotients obtained in each step. Quotient: 3x^2 + 2x  5

The remainder is the final result after all divisions. Remainder: 8
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