The result of the division is x+16. So, (x^2 +8x+1)÷(x−4)=x+16.
To perform synthetic division, we'll be dividing the polynomial
x^2 +8x+1 by the binomial x−4. The synthetic division process involves setting up a table and performing a series of calculations.
The dividend is x^2 +8x+1, and the divisor is x−4.
To use synthetic division, we'll use the root x=4 because the divisor is x−4.
Here's the setup:
4 | 1 8 1
Now, bring down the first coefficient:
4 | 1 8 1
-----------------
|
Multiply the divisor (4) by the first term (1) and write the result below the line:
4 | 1 8 1
-----------------
| 4
Add the corresponding terms:
4 | 1 8 1
-----------------
| 4
-----------
1 12
Repeat the process:
4 | 1 8 1
-----------------
| 4
-----------
1 12
---------
1 16
Now, the numbers in the bottom row represent the coefficients of the quotient. So, the quotient is 1x+16, and the remainder is 0. Therefore, the result of the division is x+16.
So, (x^2 +8x+1)÷(x−4)=x+16.