How do you divide #(x^3+7x^2-4x-1)/(3x-1) #?

Degree higher than < degree lower.

To divide (x^3+7x^2-4x-1) by (3x-1), you can use long division. Here are the steps:

1. Divide the first term of the numerator (x^3) by the first term of the denominator (3x). The result is (1/3)x^2.

2. Multiply the entire denominator (3x-1) by the result from step 1, which is (1/3)x^2. This gives you (1/3)x^3 - (1/3)x^2.

3. Subtract the result from step 2 from the original numerator (x^3+7x^2-4x-1). This gives you (7/3)x^2 - 4x - 1.

4. Bring down the next term from the original numerator, which is -4x.

5. Divide the first term of the new numerator ((7/3)x^2) by the first term of the denominator (3x). The result is (7/9)x.

6. Multiply the entire denominator (3x-1) by the result from step 5, which is (7/9)x. This gives you (7/9)x^2 - (7/9)x.

7. Subtract the result from step 6 from the new numerator ((7/3)x^2 - 4x - 1). This gives you (-4/9)x - 1.

8. Bring down the next term from the original numerator, which is -1.

9. Divide the first term of the new numerator ((-4/9)x) by the first term of the denominator (3x). The result is (-4/27).

10. Multiply the entire denominator (3x-1) by the result from step 9, which is (-4/27). This gives you (-4/27)x - (-4/27).

11. Subtract the result from step 10 from the new numerator ((-4/9)x - 1). This gives you (-4/27) + (-4/27).

12. The final result of the division is (1/3)x^2 + (7/9)x - (4/27).

Therefore, (x^3+7x^2-4x-1)/(3x-1) = (1/3)x^2 + (7/9)x - (4/27).