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If g(y)=7y215y14g(y) = 7y^2 - 15y - 14, use synthetic division to find g(2)g(2).

Full solution

Q. If g(y)=7y215y14g(y) = 7y^2 - 15y - 14, use synthetic division to find g(2)g(2).
  1. Write Coefficients and Value: To use synthetic division, we first write down the coefficients of the polynomial: 77, 15-15, and 14-14. Then we write the value we are evaluating, which is 22, to the left.
  2. Bring Down First Coefficient: We bring down the first coefficient, 77, as it is.
  3. Multiply and Write Result: Multiply the value we brought down 77 by 22 (the value we are evaluating at) and write the result under the second coefficient. So, 7×2=147 \times 2 = 14.
  4. Add Second Coefficient: Add the second coefficient (15-15) to the result from the previous step (1414) and write the sum under it. So, 15+14=1-15 + 14 = -1.
  5. Multiply and Write Result: Multiply the result from the previous step (1-1) by 22 and write the result under the third coefficient. So, 1×2=2-1 \times 2 = -2.
  6. Add Third Coefficient: Add the third coefficient (14-14) to the result from the previous step (2-2) and write the sum under it. So, 14+2=16-14 + -2 = -16.

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