Divide. If there is a remainder, include it as a simplified fraction. (4z^3 + 10z^2 - 24z) ÷ (z + 4) ______

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Divide. If there is a remainder, include it as a simplified fraction.   (4z^3 + 10z^2 - 24z) ÷ (z + 4)    ______

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Use Polynomial Long Division: To divide the polynomial (4z^3 + 10z^2 - 24z) by the binomial (z + 4), we will use polynomial long division.Find First Quotient Term: First, we divide the leading term of the polynomial, 4z^3, by the leading term of the binomial, z, to get the first term of the quotient, which is 4z^2. Calculation: 4z^3 ÷ z = 4z^2Subtract and Multiply: Next, we multiply the entire binomial (z + 4) by the term we just found, 4z^2, and subtract the result from the original polynomial. Calculation: (z + 4) * 4z^2 = 4z^3 + 16z^2 Subtraction: (4z^3 + 10z^2 - 24z) - (4z^3 + 16z^2) = -6z^2 - 24zFind Next Quotient Term: Now, we divide the leading term of the new polynomial, -6z^2, by the leading term of the binomial, z, to get the next term of the quotient, which is -6z. Calculation: -6z^2 ÷ z = -6zRepeat Subtraction and Multiplication: We multiply the entire binomial (z + 4) by the term we just found, -6z, and subtract the result from the new polynomial. Calculation: (z + 4) * -6z = -6z^2 - 24z Subtraction: (-6z^2 - 24z) - (-6z^2 - 24z) = 0Complete Division: Since we have no remainder, the division is complete, and the quotient is the final answer.

Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(4z^3 + 10z^2 - 24z) \div (z + 4)$

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Divide. If there is a remainder, include it as a simplified fraction.\newline(4z3+10z2−24z)÷(z+4)(4z^3 + 10z^2 - 24z) \div (z + 4)(4z3+10z2−24z)÷(z+4)

Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(4z^3 + 10z^2 - 24z) \div (z + 4)$