Find the quotient and remainder using polynomial long division. (2x^(3)-12x^(2)+7x-28)/(2x^(2)+5) The quotient is The remainder is

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Find the quotient and remainder using polynomial long division.  (2x^(3)-12x^(2)+7x-28)/(2x^(2)+5) The quotient is The remainder is

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Perform Division: We will perform polynomial long division to find the quotient and remainder when dividing (2x^(3)-12x^(2)+7x-28) by (2x^(2)+5). First, we divide the leading term of the dividend, 2x^(3), by the leading term of the divisor, 2x^(2), to find the first term of the quotient. 2x^(3) ÷ 2x^(2) = x.Find First Term: We multiply the entire divisor (2x^(2)+5) by the term we just found, x, and subtract the result from the dividend. (2x^(2)+5) * x = 2x^(3) + 5x. Subtract this from the dividend: (2x^(3)-12x^(2)+7x-28) - (2x^(3) + 5x) = -12x^(2) + 7x - 5x - 28 = -12x^(2) + 2x - 28.Subtract Result: We bring down the next term of the dividend, which is already included in the subtraction result, and repeat the division process. Now we divide the leading term of the new polynomial, -12x^(2), by the leading term of the divisor, 2x^(2). -12x^(2) ÷ 2x^(2) = -6.Repeat Division: We multiply the entire divisor (2x^(2)+5) by the term we just found, -6, and subtract the result from the new polynomial. (2x^(2)+5) * (-6) = -12x^(2) - 30. Subtract this from the new polynomial: (-12x^(2) + 2x - 28) - (-12x^(2) - 30) = -12x^(2) + 12x^(2) + 2x - 28 + 30 = 2x + 2.Find Next Term: Since the degree of the remaining polynomial (2x + 2) is less than the degree of the divisor (2x^(2)+5), we cannot continue the division process. Therefore, 2x + 2 is the remainder.Finalize Division: The quotient of the division is the sum of the terms we found: x - 6. The remainder is the last polynomial we obtained: 2x + 2.

Find the quotient and remainder using polynomial long division. $\newline$ $(2x^{3}-12x^{2}+7x-28)/(2x^{2}+5)$ $\newline$ The quotient is $\newline$ The remainder is

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Find the quotient and remainder using polynomial long division.\newline(2x3−12x2+7x−28)/(2x2+5)(2x^{3}-12x^{2}+7x-28)/(2x^{2}+5)(2x3−12x2+7x−28)/(2x2+5)\newlineThe quotient is\newlineThe remainder is

Find the quotient and remainder using polynomial long division. $\newline$ $(2x^{3}-12x^{2}+7x-28)/(2x^{2}+5)$ $\newline$ The quotient is $\newline$ The remainder is