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Divide. If there is a remainder, include it as a simplified fraction.\newline(2j3+8j242j)÷(j+7)(2j^3 + 8j^2 - 42j) \div (j + 7)\newline______

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Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(2j3+8j242j)÷(j+7)(2j^3 + 8j^2 - 42j) \div (j + 7)\newline______
  1. Divide by First Term: We will use polynomial long division to divide (2j3+8j242j)(2j^3 + 8j^2 - 42j) by (j+7)(j + 7). First, we divide the first term of the dividend, 2j32j^3, by the first term of the divisor, jj, to get the first term of the quotient. 2j3÷j=2j22j^3 \div j = 2j^2
  2. Multiply and Subtract: Now, we multiply the entire divisor (j+7)(j + 7) by the first term of the quotient (2j2)(2j^2) and subtract the result from the original polynomial.(2j2)(j+7)=2j3+14j2(2j^2)(j + 7) = 2j^3 + 14j^2Subtract this from the original polynomial:(2j3+8j242j)(2j3+14j2)=6j242j(2j^3 + 8j^2 - 42j) - (2j^3 + 14j^2) = -6j^2 - 42j
  3. Divide New Leading Term: Next, we divide the new leading term, 6j2-6j^2, by the leading term of the divisor, jj, to get the next term of the quotient.\newline6j2÷j=6j-6j^2 \div j = -6j
  4. Multiply and Subtract Again: We multiply the entire divisor (j+7)(j + 7) by the new term of the quotient (6j)(-6j) and subtract the result from the remaining polynomial.\newline(6j)(j+7)=6j242j(-6j)(j + 7) = -6j^2 - 42j\newlineSubtract this from the remaining polynomial:\newline(6j242j)(6j242j)=0(-6j^2 - 42j) - (-6j^2 - 42j) = 0
  5. Check for Remainder: Since the remainder is 00, we have divided the polynomial completely, and there is no remainder to express as a fraction.

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