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Divide. If the polynomial does not divide evenly, include the remainder as a fraction.\newline(5w2+24w+21)÷(w+3)(5w^2 + 24w + 21) \div (w + 3)\newline_____

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Q. Divide. If the polynomial does not divide evenly, include the remainder as a fraction.\newline(5w2+24w+21)÷(w+3)(5w^2 + 24w + 21) \div (w + 3)\newline_____
  1. Divide First Term: Divide the first term of the dividend by the first term of the divisor: 5w2÷w=5w5w^2 \div w = 5w.
  2. Multiply by 5w5w: Multiply the divisor by 5w5w: (w+3)(5w)=5w2+15w(w + 3)(5w) = 5w^2 + 15w.
  3. Subtract Result: Subtract the result from the dividend: 5w2+24w+215w^2 + 24w + 21 - 5w2+15w5w^2 + 15w = (9\)w + 2121\
  4. Divide New First Term: Divide the new first term of the remainder by the first term of the divisor: 9w÷w=99w \div w = 9.
  5. Multiply by 99: Multiply the divisor by 99: (w+3)(9)=9w+27(w + 3)(9) = 9w + 27.
  6. Subtract Result: Subtract the result from the remainder: (9w+21)(9w+27)=6(9w + 21) - (9w + 27) = -6.
  7. Include Remainder: Since 6-6 is less than the degree of the divisor (w+3)(w + 3), we include the remainder as a fraction: 6÷(w+3)-6 \div (w + 3).

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