Q. If h(u)=7u2+21u+1, use synthetic division to find h(−4).
Write Coefficients and Divisor: Write down the coefficients of the polynomial h(u) and the value we are dividing by, which is −4.
Set Up Synthetic Division: Set up the synthetic division: −4∣7211
Bring Down Leading Coefficient: Bring down the leading coefficient to the bottom row.−4∣72117
Multiply and Write Result: Multiply −4 by 7 and write the result under the second coefficient.−4∣7211−4∣7−28
Add Numbers in Second Column: Add the numbers in the second column: 21+(−28)=−7.−4∣72117−28−7
Multiply and Write Result: Multiply −4 by −7 and write the result under the third coefficient.−4∣7211−4∣7−28−4∣7−728
Add Numbers in Third Column: Add the numbers in the third column: 1+28=29.−4∣72117−28−72829
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).
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