Video Transcript
Use synthetic substitution to find the value of ๐ of 20 given ๐ of ๐ฅ equals 0.06๐ฅ to the fourth minus 0.14๐ฅ cubed minus 3.1๐ฅ plus 5.4.
To set up synthetic substitution, we start with the value of ๐ฅ that weโre trying to solve for, in this case 20. And then, we take the coefficients from each term: 0.06 from ๐ฅ to the fourth, negative 0.14 from ๐ฅ cubed. Now, this is important. Notice that weโre adding the coefficients from each ๐ฅ term with descending exponent values. We have to do this for every ๐ฅ term.
The function weโre given does not have a coefficient with ๐ฅ squared. So we add a zero there as a placeholder to represent the ๐ฅ squared term. From there, we have negative 3.1๐ฅ and ๐ฅ to the zero power would be the constant 5.4.
And now, weโre ready to solve. The first step is to bring down our 0.06. Then, weโre going to multiply 20 by 0.06. 20 times 0.06 is 1.2. Now, weโre going to add negative 0.14 and 1.2 which equals 1.06. Now, we multiply 20 times 1.06 which equals 21.2. 21.2 plus zero equals 21.2. Multiply 21.2 by 20 and we get 424. 424 plus negative 3.1 equals 420.9. Multiply this value, 420.9 by 20 and we get 8418. Add 5.4 to that value and you get 8423.4.
The value of the function given at 20 equals 8423.4. Pretty cool, right?
