Use synthetic division to find ƒ(2). ƒ(x)=5x^4-12x^2+2x-8

Question

Accepted Answer

Hey, everyone here we are given that for the given polynomial function, use synthetic division to find F of one. Here. Our given polynomial function is F of X is equal to seven X to the fourth power minus 16 X squared plus nine, X minus 10. Here we have four answer, choice options, answer choice, A 10, answer B negative 10, answer C zero and answer choice D 20. So to begin solving this problem, we first need to set up our table synthetic division. So we first just have a vertical line and then a horizontal line that crosses through it. And since we are trying to find F of one to the left side of our vertical line, we place this value of X which is one. And then to the right of our vertical line, we place each of the coefficients of X starting with the coefficient of the highest power of X. Here we have the highest power of four. So the coefficient of X to the fourth power is seven. Now we move on to X cubed which we see does not appear in our function. So its coefficient is zero, then moving on to X squared, we have negative 16 moving on to X, we have the coefficient of nine. And lastly the coefficient of X to the zeroth power or just our constant value is negative 10. And thus our last coefficient that we write down and now that we have finished setting up our table here, we can begin performing synthetic division. So the first step is to just bring down the first constant or the first coefficient which is seven and rewrite it underneath the horizontal line. We now take this value of seven and multiply it by the value on the left side of the vertical line, which is one. So we have seven times one which gives us seven. We now add this value to the coefficient in the second column which is zero. So we have zero plus seven which gives us seven. Repeating this process. We now take seven again and multiply it by one, this gives us seven and now we add seven to the coefficient in the third column which is negative 17. So we have negative 17 plus seven which gives us negative nine. Repeating this process. We have negative nine times one which is just negative nine. We now have negative nine plus nine which just gives us zero and repeating this process one more time. We have now zero times one which is just zero, then we add it to our last coefficient. So we have negative 10 plus zero which is negative 10. So now that we have finished performing synthetic division, as we recall, we were trying to find F of one. Well, this value is just going to be the last value we obtained from synthetic division, which in this case is negative 10. So we see F of one is two negative 10. So with this solution, we are left with answer choice B where again, our final value here is negative 10. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Use synthetic division to find ƒ(2). ƒ(x)=5x^4-12x^2+2x-8

Key Concepts

Synthetic Division

Polynomial Evaluation

Coefficients and Degree of a Polynomial