Divide using long division or synthetic division.
(21x^3 - 7)/(3x - 1)
This is what I have so far, but I am having a hard time with what to do next.
3x-1/ 7(3x^3-1)
To divide the polynomial (21x^3 - 7) by (3x - 1) using long division, follow these steps:
1. Write the dividend (21x^3 - 7) and divisor (3x - 1) in the long division format, with the dividend inside the division symbol and the divisor outside:
```
_______
3x - 1) 21x^3 - 7
```
2. Look at the leading term of the dividend (21x^3) and divide it by the leading term of the divisor (3x). Write the result above the line:
```
7x^2
_______
3x - 1) 21x^3 - 7
```
3. Multiply the entire divisor (3x - 1) by the result obtained in step 2 (7x^2). Write the product below the line, aligned with the dividend term of the same degree:
```
7x^2
_______
3x - 1) 21x^3 - 7
- (21x^3 - 7x^2)
```
4. Subtract the product obtained in step 3 from the corresponding terms of the dividend. Write the result below the line:
```
7x^2
_______
3x - 1) 21x^3 - 7
- (21x^3 - 7x^2)
_____________
0 + 7x^2 - 7
```
5. Bring down the next term of the dividend (-7), and repeat steps 2 to 4 with this new term:
```
7x^2 + (7)
_______
3x - 1) 21x^3 - 7
- (21x^3 - 7x^2)
_____________
0 + 7x^2 - 7
- (7x^2 - 7)
_____________
0
```
6. The remaining result is zero, indicating that there is no remainder. The quotient obtained so far is 7x^2 + 7.