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Divide. If the polynomial does not divide evenly, include the remainder as a fraction.\newline(19w2+143w76)÷(w+8)(19w^2 + 143w - 76) \div (w + 8)\newline_____

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Q. Divide. If the polynomial does not divide evenly, include the remainder as a fraction.\newline(19w2+143w76)÷(w+8)(19w^2 + 143w - 76) \div (w + 8)\newline_____
  1. Multiply and Subtract: Multiply the divisor w+8w + 8 by the quotient found 19w19w to subtract from the dividend.19w×(w+8)=19w2+152w.19w \times (w + 8) = 19w^2 + 152w.
  2. Subtract Result: Subtract the result from the dividend.\newline(19w2+143w76)(19w2+152w)=9w76(19w^2 + 143w - 76) - (19w^2 + 152w) = -9w - 76.
  3. Divide First Term: Divide the new first term of the remainder by the first term of the divisor.\newline(9w)÷(w)=9(-9w) \div (w) = -9.
  4. Multiply and Subtract Again: Multiply the divisor w+8w + 8 by the new quotient found 9 -9 to subtract from the remainder.9×(w+8)=9w72. -9 \times (w + 8) = -9w - 72.
  5. Subtract Result Again: Subtract the result from the remainder.\newline(9w76)(9w72)=4(-9w - 76) - (-9w - 72) = -4.
  6. Final Quotient and Remainder: Since 4-4 is less than the degree of the divisor (w+8)(w + 8), we cannot divide further, so 4-4 is the remainder.\newlineThe final quotient is 19w919w - 9 with a remainder of 4-4.

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