Check Factor: Check if 4c−7 is a factor of the polynomial by using synthetic division or long division.Let's do synthetic division.First, find the zero of 4c−7, which is c=47.
Synthetic Division Setup: Set up synthetic division with 47 and the coefficients of the polynomial: 4,−27,0,35. Remember to include the 0 for the missing c term.
Bring Down Coefficient: Bring down the first coefficient, 4. Multiply 47 by 4 and write the result under the second coefficient, −27.
Add Second Column: Add the second column: −27+(47)⋅4=−27+7=−20.
Multiply and Add: Multiply 47 by −20 and write the result under the next coefficient, 0.
Correct Third Column: Add the third column: 0+(47)(−20)=−35. Oops, this should be 0+(47)(−20)=0−35=−35.
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