Divide. If there is a remainder, include it as a simplified fraction. (4n^3 + 22n^2 - 12n) ÷ (n + 6) ______

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Divide. If there is a remainder, include it as a simplified fraction.   (4n^3 + 22n^2 - 12n) ÷ (n + 6)    ______

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Divide by First Term: We will use polynomial long division to divide (4n^3 + 22n^2 - 12n) by (n + 6). First, we divide the first term of the dividend, 4n^3, by the first term of the divisor, n, to get the first term of the quotient. 4n^3 ÷ n = 4n^2Subtract and Simplify: We multiply the divisor (n + 6) by the first term of the quotient (4n^2) and subtract the result from the dividend. (4n^3 + 22n^2 - 12n) - (4n^2 * (n + 6)) = (4n^3 + 22n^2 - 12n) - (4n^3 + 24n^2) This simplifies to -2n^2 - 12n.Divide New Leading Term: Next, we divide the new leading term of the remaining polynomial, -2n^2, by the first term of the divisor, n. -2n^2 ÷ n = -2nSubtract and Simplify: We multiply the divisor (n + 6) by the new term of the quotient (-2n) and subtract the result from the remaining polynomial. (-2n^2 - 12n) - (-2n * (n + 6)) = (-2n^2 - 12n) - (-2n^2 - 12n) This simplifies to 0, meaning there is no remainder.Final Quotient: The quotient we have found is 4n^2 - 2n, and there is no remainder. Therefore, the division is complete.

Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(4n^3 + 22n^2 - 12n) \div (n + 6)$ $\newline$ ______

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Divide. If there is a remainder, include it as a simplified fraction.\newline(4n3+22n2−12n)÷(n+6)(4n^3 + 22n^2 - 12n) \div (n + 6)(4n3+22n2−12n)÷(n+6)\newline______

Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(4n^3 + 22n^2 - 12n) \div (n + 6)$ $\newline$ ______