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If p(w)=9w2+22w30p(w) = 9w^2 + 22w - 30, use synthetic division to find p(2)p(-2).

Full solution

Q. If p(w)=9w2+22w30p(w) = 9w^2 + 22w - 30, use synthetic division to find p(2)p(-2).
  1. Set up synthetic division: Set up synthetic division with 2-2 outside the division box and the coefficients of p(w)p(w) inside: 99, 2222, 30-30.
  2. Bring down leading coefficient: Bring down the leading coefficient, 99, to the bottom row.
  3. Multiply and write result: Multiply 2-2 by 99 and write the result, 18-18, under the second coefficient, 2222.
  4. Add coefficients: Add the second coefficient, 2222, and the number just written, 18-18, to get 44. Write this under the line.
  5. Multiply and write result: Multiply 2-2 by the number just written, 44, to get 8-8. Write this under the third coefficient, 30-30.
  6. Add coefficients: Add the third coefficient, 30-30, and the number just written, 8-8, to get 38-38. Write this under the line.
  7. Find value of p(2)p(-2): The number at the bottom right, 38-38, is the value of p(2)p(-2).

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