How do you divide #(6x^4+4x^3-12x^2-7x-7)/(x-2) #?

Question

How do you divide #(6x^4+4x^3-12x^2-7x-7)/(x-2)  #?

Abigail Allen · Accepted Answer

#color(blue)(6x^3 + 16x^2 + 20x + 33 + 59/(x-2))#

Hope you find this solution useful.

Please find below my solution which has the desired format:

Savannah Anderson · Answer

undefined To divide (6x^4+4x^3-12x^2-7x-7) by (x-2), you can use long division. Here are the steps:

1. Divide the first term of the dividend (6x^4) by the first term of the divisor (x). The result is 6x^3.
2. Multiply the entire divisor (x-2) by the result obtained in step 1 (6x^3). The result is 6x^4-12x^3.
3. Subtract the result obtained in step 2 from the original dividend (6x^4+4x^3-12x^2-7x-7) to get the new dividend: (4x^3-12x^2-7x-7).
4. Bring down the next term from the original dividend, which is -12x^2.
5. Divide the new dividend (4x^3-12x^2-7x-7) by the first term of the divisor (x). The result is 4x^2.
6. Multiply the entire divisor (x-2) by the result obtained in step 5 (4x^2). The result is 4x^3-8x^2.
7. Subtract the result obtained in step 6 from the new dividend (4x^3-12x^2-7x-7) to get the new dividend: (-4x^2-7x-7).
8. Bring down the next term from the new dividend, which is -7x.
9. Divide the new dividend (-4x^2-7x-7) by the first term of the divisor (x). The result is -4x.
10. Multiply the entire divisor (x-2) by the result obtained in step 9 (-4x). The result is -4x^2+8x.
11. Subtract the result obtained in step 10 from the new dividend (-4x^2-7x-7) to get the new dividend: (-15x-7).
12. Bring down the next term from the new dividend, which is -15x.
13. Divide the new dividend (-15x-7) by the first term of the divisor (x). The result is -15.
14. Multiply the entire divisor (x-2) by the result obtained in step 13 (-15). The result is -15x+30.
15. Subtract the result obtained in step 14 from the new dividend (-15x-7) to get the remainder: (-37).

Therefore, the quotient is 6x^3+4x^2-4x-15, and the remainder is -37.