Divide using synthetic division, step by step.
(x^4-12x^2-5)divide(x+13)
To divide the polynomial x^4 - 12x^2 - 5 by x + 13 using synthetic division, we will follow these steps:
Step 1: Set up synthetic division. Write down all the coefficients of the dividend (the polynomial being divided) in decreasing order of degree. Make sure to include a placeholder for missing terms. In this case, the dividend is x^4 - 12x^2 - 5, so the coefficients are 1, 0, -12, 0, -5. The divisor is x + 13.
```
1 0 -12 0 -5
```
Step 2: Write down the negative value of the divisor. In this case, the negative value of x + 13 is -13.
```
1 0 -12 0 -5
-13
```
Step 3: Draw a line underneath the coefficients.
```
1 0 -12 0 -5
-13
```
________
Step 4: Bring down the first coefficient (1) directly below the line.
```
1 0 -12 0 -5
-13
_______
1
```
Step 5: Multiply the negative value of the divisor (-13) by the number at the bottom and write the result above the next coefficient (-12).
```
1 0 -12 0 -5
-13
_______
1
-13
```
Step 6: Add the two numbers above the line (-12 + -13 = -25) and write the result below the line.
```
1 0 -12 0 -5
-13
_______
1
-13
______
-25
```
Step 7: Repeat steps 5 and 6 until all coefficients have been processed.
```
1 0 -12 0 -5
-13
_______
1
-13
______
-25 325
______
```
Step 8: The numbers below the line represent the coefficients of the quotient polynomial. In this case, the quotient polynomial is x^3 - 13x^2 - 25x + 325.
Therefore, the result of dividing x^4 - 12x^2 - 5 by x + 13 using synthetic division is x^3 - 13x^2 - 25x + 325.