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(4c^(3)-27c^(2)+35 c)÷(4c-7)

(4c327c2+35c)÷(4c7) \left(4 c^{3}-27 c^{2}+35 c\right) \div(4 c-7)

Full solution

Q. (4c327c2+35c)÷(4c7) \left(4 c^{3}-27 c^{2}+35 c\right) \div(4 c-7)
  1. Check Factor: Check if 4c74c-7 is a factor of the polynomial by using synthetic division or long division.\newlineLet's do synthetic division.\newlineFirst, find the zero of 4c74c-7, which is c=74c=\frac{7}{4}.
  2. Synthetic Division Setup: Set up synthetic division with 74\frac{7}{4} and the coefficients of the polynomial: 4,27,0,354, -27, 0, 35. Remember to include the 00 for the missing cc term.
  3. Bring Down Coefficient: Bring down the first coefficient, 44. Multiply 74\frac{7}{4} by 44 and write the result under the second coefficient, 27-27.
  4. Add Second Column: Add the second column: 27+(74)4=27+7=20-27 + (\frac{7}{4})\cdot4 = -27 + 7 = -20.
  5. Multiply and Add: Multiply 74\frac{7}{4} by 20-20 and write the result under the next coefficient, 00.
  6. Correct Third Column: Add the third column: 0+(74)(20)=350 + \left(\frac{7}{4}\right)(-20) = -35. Oops, this should be 0+(74)(20)=035=350 + \left(\frac{7}{4}\right)(-20) = 0 - 35 = -35.

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