Complete the synthetic division problem below. What is the quotient in polynomial form?
Accepted Solution
A:
The polynomial would be 2x+5.
We bring down the first number inside the box, 2, unchanged.
_______ -1| 2 7 5 _______ 2
Now we multiply that 2 by the number outside, -1: _______ -1| 2 7 5 -2 2
Now we add the two numbers in the middle column: ________ -1| 2 7 5 -2 2 5
Multiply the 5 we brought down by the -1: ________ -1| 2 7 5 -2 -5 2 5
Add the numbers in the last column: ________ -1| 2 7 5 -2 -5 2 5 0
The 3 numbers under the box represent the coefficients of x² and x, as well as the constant. When we finish, we no longer have an x², but start at the next level down, which would be x. 2 would be the coefficient of x and 5 would be the constant, with 0 remainder.