(6x^4-x^3+11x^2-2x-2)/(3x+1)
i don't know to solve it
Is there multiple answers for this? If so, can you post them, it will be able to help me.
Also, what are you supposed to be solving for? Are you solving for x?
To solve the expression (6x^4 - x^3 + 11x^2 - 2x - 2)/(3x + 1), we can use long division. This method involves dividing each term of the numerator by the denominator to find the quotient.
Let's go step by step:
1. Start by dividing the first term of the numerator (6x^4) by the first term of the denominator (3x). The result is 2x^3.
2. Multiply the entire denominator (3x + 1) by the result from the previous step, 2x^3. This gives us 6x^4 + 2x^3.
3. Subtract the result from step 2 from the numerator (6x^4 - 2x^3), which leaves us with -3x^3 + 11x^2 - 2x - 2.
4. Bring down the next term from the numerator, which is 0x^2.
5. Divide the first term of the new numerator (-3x^3) by the first term of the denominator (3x), giving us -x^2.
6. Multiply the entire denominator (3x + 1) by the result from step 5, -x^2. This gives us -3x^3 - x^2.
7. Subtract the result from step 6 from the new numerator (-3x^3 + x^2), which leaves us with 12x^2 - 2x - 2.
8. Bring down the next term from the numerator, which is 0x.
9. Divide the first term of the new numerator (12x^2) by the first term of the denominator (3x), giving us 4x.
10. Multiply the entire denominator (3x + 1) by the result from step 9, 4x. This gives us 12x^2 + 4x.
11. Subtract the result from step 10 from the new numerator (12x^2 - 4x), which leaves us with -6x - 2.
12. Bring down the next term from the numerator, which is -2.
13. Divide the first term of the new numerator (-6x) by the first term of the denominator (3x), giving us -2.
14. Multiply the entire denominator (3x + 1) by the result from step 13, -2. This gives us -6x - 2.
15. Subtract the result from step 14 from the new numerator (-6x - 2), which leaves us with 0.
Now, since the new numerator is zero, we have no remainder. The quotient is the result of all the division steps, which is 2x^3 - x^2 + 4x - 2.
Therefore, the simplified expression is (6x^4 - x^3 + 11x^2 - 2x - 2)/(3x + 1) = 2x^3 - x^2 + 4x - 2.