How do you divide #(-x^3+12x^2-12x+15) / (x-31)
# using polynomial long division?

Question

How do you divide #(-x^3+12x^2-12x+15) / (x-31) 
# using polynomial long division?

Kennedy Adams · Accepted Answer

#-x^2 - 19x - 601, R -18616#

like so

Hazel Anglin · Answer

undefined To divide (-x^3+12x^2-12x+15) by (x-31) using polynomial long division, follow these steps:

1. Arrange the dividend and divisor in descending order of exponents: -x^3+12x^2-12x+15 divided by x-31.

2. Divide the first term of the dividend (-x^3) by the first term of the divisor (x). The result is -x^2.

3. Multiply the divisor (x-31) by the quotient obtained in step 2 (-x^2). The result is -x^3+31x^2.

4. Subtract the product obtained in step 3 from the dividend (-x^3+12x^2-12x+15) to get the new dividend: 12x^2-12x+15-(-x^3+31x^2).

5. Bring down the next term of the dividend (-12x) and repeat steps 2-4.

6. Divide the first term of the new dividend (12x^2) by the first term of the divisor (x). The result is 12x.

7. Multiply the divisor (x-31) by the quotient obtained in step 6 (12x). The result is 12x^2-372x.

8. Subtract the product obtained in step 7 from the new dividend (12x^2-12x+15-(-x^3+31x^2)) to get the new dividend: -384x+15.

9. Bring down the next term of the new dividend (15) and repeat steps 2-4.

10. Divide the first term of the new dividend (-384x) by the first term of the divisor (x). The result is -384.

11. Multiply the divisor (x-31) by the quotient obtained in step 10 (-384). The result is -384x+11904.

12. Subtract the product obtained in step 11 from the new dividend (-384x+15-(-384x+11904)) to get the remainder: -11889.

The quotient is -x^2+12x+384 and the remainder is -11889.