Divide. If there is a remainder, include it as a simplified fraction. (2j^3 + 8j^2 - 42j) ÷ (j + 7) ______

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Divide. If there is a remainder, include it as a simplified fraction.   (2j^3 + 8j^2 - 42j) ÷ (j + 7)    ______

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Divide by First Term: We will use polynomial long division to divide (2j^3 + 8j^2 - 42j) by (j + 7). First, we divide the first term of the dividend, 2j^3, by the first term of the divisor, j, to get the first term of the quotient. 2j^3 ÷ j = 2j^2Multiply and Subtract: Now, we multiply the entire divisor (j + 7) by the first term of the quotient (2j^2) and subtract the result from the original polynomial. (2j^2)(j + 7) = 2j^3 + 14j^2 Subtract this from the original polynomial: (2j^3 + 8j^2 - 42j) - (2j^3 + 14j^2) = -6j^2 - 42jDivide New Leading Term: Next, we divide the new leading term, -6j^2, by the leading term of the divisor, j, to get the next term of the quotient. -6j^2 ÷ j = -6jMultiply and Subtract Again: We multiply the entire divisor (j + 7) by the new term of the quotient (-6j) and subtract the result from the remaining polynomial. (-6j)(j + 7) = -6j^2 - 42j Subtract this from the remaining polynomial: (-6j^2 - 42j) - (-6j^2 - 42j) = 0Check for Remainder: Since the remainder is 0, we have divided the polynomial completely, and there is no remainder to express as a fraction.

Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(2j^3 + 8j^2 - 42j) \div (j + 7)$ $\newline$ ______

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Divide. If there is a remainder, include it as a simplified fraction.\newline(2j3+8j2−42j)÷(j+7)(2j^3 + 8j^2 - 42j) \div (j + 7)(2j3+8j2−42j)÷(j+7)\newline______

Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(2j^3 + 8j^2 - 42j) \div (j + 7)$ $\newline$ ______