Divide. If there is a remainder, include it as a simplified fraction. (k^3 + 4k^2 - 5k) ÷ (k - 1) ______

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Divide. If there is a remainder, include it as a simplified fraction.   (k^3 + 4k^2 - 5k) ÷ (k - 1)    ______

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Divide by k: We will use polynomial long division to divide (k^3 + 4k^2 - 5k) by (k - 1). First, we divide the first term of the dividend, k^3, by the first term of the divisor, k, to get the first term of the quotient. k^3 ÷ k = k^2Subtract and Multiply: We multiply the divisor (k - 1) by the first term of the quotient (k^2) and subtract the result from the dividend. (k - 1) * k^2 = k^3 - k^2 Subtract this from the dividend: (k^3 + 4k^2 - 5k) - (k^3 - k^2) = 4k^2 - k^2 - 5k = 3k^2 - 5kDivide 3k^2 by k: Next, we divide the first term of the new dividend, 3k^2, by the first term of the divisor, k, to get the next term of the quotient. 3k^2 ÷ k = 3kSubtract and Multiply: We multiply the divisor (k - 1) by the new term of the quotient (3k) and subtract the result from the new dividend. (k - 1) * 3k = 3k^2 - 3k Subtract this from the new dividend: (3k^2 - 5k) - (3k^2 - 3k) = -5k + 3k = -2kDivide -2k by k: Now, we divide the first term of the new dividend, -2k, by the first term of the divisor, k, to get the next term of the quotient. -2k ÷ k = -2Subtract and Multiply: We multiply the divisor (k - 1) by the new term of the quotient (-2) and subtract the result from the new dividend. (k - 1) * (-2) = -2k + 2 Subtract this from the new dividend: (-2k) - (-2k + 2) = -2k + 2k - 2 = -2Final Remainder: Since the degree of the remainder (-2) is less than the degree of the divisor (k - 1), we cannot continue the division process. The remainder is -2.

Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(k^3 + 4k^2 - 5k) \div (k - 1)$ $\newline$ ______

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Divide. If there is a remainder, include it as a simplified fraction.\newline(k3+4k2−5k)÷(k−1)(k^3 + 4k^2 - 5k) \div (k - 1)(k3+4k2−5k)÷(k−1)\newline______

Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(k^3 + 4k^2 - 5k) \div (k - 1)$ $\newline$ ______