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If h(u)=7u2+21u+1h(u) = 7u^2 + 21u + 1, use synthetic division to find h(4)h(-4).

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Q. If h(u)=7u2+21u+1h(u) = 7u^2 + 21u + 1, use synthetic division to find h(4)h(-4).
  1. Write Coefficients and Divisor: Write down the coefficients of the polynomial h(u)h(u) and the value we are dividing by, which is 4-4.
  2. Set Up Synthetic Division: Set up the synthetic division: \newline47211-4 | 7 21 1
  3. Bring Down Leading Coefficient: Bring down the leading coefficient to the bottom row.\newline47211-4 | 7 21 1\newline 77
  4. Multiply and Write Result: Multiply 4-4 by 77 and write the result under the second coefficient.\newline47211-4 \mid 7 \quad 21 \quad 1\newline4728\phantom{-4 \mid} 7 \quad -28
  5. Add Numbers in Second Column: Add the numbers in the second column: 21+(28)=721 + (-28) = -7.\newline47-4 | 7 2121 11\newline 77 28-28\newline 7-7
  6. Multiply and Write Result: Multiply 4-4 by 7-7 and write the result under the third coefficient.\newline47211-4 \,|\, 7 \, 21 \, 1\newline4728\phantom{-4 \,|\,} 7 \, -28\newline47728\phantom{-4 \,|\, 7 \,} -7 \, 28
  7. Add Numbers in Third Column: Add the numbers in the third column: 1+28=291 + 28 = 29.47211-4 | 7 21 17287 -28728-7 282929
  8. Get Result of Synthetic Division: The bottom row gives us the result of the synthetic division. The last number is the remainder, which is the value of h(4)h(-4).

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