Synthetic Division

Question

Getting lost with the steps,

 

Find the following value by using synthetic division.

 

 

F(X) = 3X^4 - 2X^3 + 4X^2 + 2

 

 

F(-1)= ?

Answer 1

Hey Winston!

 

Determine our root divisor: To find our root, we solve the divisor equation x - 1 = 0. We add 1 to each side of the equation to get x - 1 + 1 = 0 + 1 T

 

Step 1: Write down our coefficients horizontally and our root of 1 to the left

Step 2: Bring down the first coefficient of 3

Step 3: Multiply our root of 1 by our last result of 3 to get 3 and put that in column 2

Step 4: Add the new entry of 3 to our coefficient of -2 to get 1 and put this in the answer column 2

Step 5: Multiply our root of 1 by our last result of 1 to get 1 and put that in column 3

Step 6: Add the new entry of 1 to our coefficient of 4 to get 5 and put this in the answer column 3

Step 7: Multiply our root of 1 by our last result of 5 to get 5 and put that in column 4

Step 8: Add the new entry of 5 to our coefficient of 0 to get 5 and put this in the answer column 4

Step 9: Multiply our root of 1 by our last result of 5 to get 5 and put that in column 5

Step 9: Multiply our root of 1 by our last result of 5 to get 5 and put that in column 5:

Our synthetic division is complete. The values in our results row form a new equation, which has a degree 1 less than our original equation shown below

Leading Answer Term = x^(4 - 1) = x^3

 

Since the last number in our result line of 7 does not equal 0, our answer will have a remainder. We take this term and divide it by our (x - r) root

 

Answer: 3x^3 + x^2 + 5x + 5 + (7/( x - 1))