Use synthetic division to find ƒ(2). ƒ(x)=2x^3-3x^2+7x-12

Question

Accepted Answer

Hey, everyone. Here we are asked to use division to find F of four for the given polynomial function F of X is equal to four X cubed minus nine X squared plus five X minus 20. Here we have four answer choice options, answer choice. A 112 answer B 152 answer C negative 112 and answer choice D negative 152. So here to start solving this problem, we first need to set up our table for synthetic division and it consists first of a vertical line and then a horizontal line that passes through it. And now to the left of the vertical line, we place the value that we are trying to find which we are trying to find F of four. So we place the value of X which is four on the left side of the vertical line. And now to the right side of the vertical line, we place each of the coefficients of X that we have from our function starting with the coefficient of the highest power of X. So we start with X cube since three is the highest power that we have. So we start by placing the coefficient of four, then we move on to X squared which has a coefficient of negative nine, then we move on to X which has a coefficient of five. And lastly, we have our constant or the coefficient of X to the zeroth power which in this case is negative 20. So now that we have set up our table, we can begin performing synthetic division. So the first step is to just bring down the first coefficient which is four and rewrite it underneath the horizontal line. Then we take this value four and we multiply it by the X value which is also four. So we have four times four which gives us 16. And now we add this product to the coefficient in the second column. So we have negative nine plus 16 which gives us seven which we write underneath the horizontal line and then repeating this process, we now take seven, multiply it by four and we get positive 28. And now we take this product and add it to the coefficient in the third column. So five plus 28 gives us 33. Now repeating this process one more time, we now have 33 times four which simplifies to 132. We then add this to the last coefficient. So we have negative 20 plus 132 which gives us 112 now, as we recall, you're trying to find F of four. So after performing synthetic division, the value of F of four is the last value that we obtained, which is 112. So here we see FA four is equal to 112. And so we are left here with answer choice. A where our, our value is 112. 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)=2x^3-3x^2+7x-12

Key Concepts

Synthetic Division

Polynomial Evaluation

Coefficients of a Polynomial