Divide.
$(2 x^{5} + 3 x^{3} + 2 x^{2} + 12 x + 4) \div (x^{2} + 2)$

Answer

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Answer

$Quotient = 2 x^{3} - 4 x^{2} + 8 x + 16, Remainder = 32 x + 36$

Steps

Step 1 ：Let's solve the given polynomial division problem: $(2 x^{5} + 3 x^{3} + 2 x^{2} + 12 x + 4) \div (x^{2} + 2)$

Step 2 ：We can solve this by using the long division method for polynomials.

Step 3 ：Performing the division, we get the quotient and the remainder.

Step 4 ：The quotient is $2 x^{3} - 4 x^{2} + 8 x + 16$ and the remainder is $32 x + 36$

Step 5 ： $Quotient = 2 x^{3} - 4 x^{2} + 8 x + 16, Remainder = 32 x + 36$