Question

Divide -10x⁴+10x³+15x²-60x+47 by 5x-5.

Answer 1

To divide -10x⁴+10x³+15x²-60x+47 by 5x-5, we use long division. The quotient is -2x³+3x-9 and the remainder is 2.

Step-by-step explanation:

To divide -10x⁴+10x³+15x²-60x+47 by 5x-5, we use long division. Here are the steps:

1. Divide -10x⁴ by 5x to get -2x³.
2. Multiply -2x³ by 5x-5 to get -10x⁴+10x³.
3. Subtract -10x⁴+10x³ from -10x⁴+10x³+15x² to get 15x².
4. Divide 15x² by 5x to get 3x.
5. Multiply 3x by 5x-5 to get 15x²-15x.
6. Subtract 15x²-15x from 15x²-15x-60x to get -45x.
7. Divide -45x by 5x to get -9.
8. Multiply -9 by 5x-5 to get -45x+45.
9. Subtract -45x+45 from -45x+47 to get 2.

So the quotient is -2x³+3x-9 and the remainder is 2.