Final answer:
To divide (8x³ - 10x² + 9x-10) ÷ (2x - 1) using long division, divide each term of the numerator by the first term of the denominator and subtract the result. Repeat the process until all terms have been divided. The quotient is the final result with a remainder.
Step-by-step explanation:
Long Division of Polynomials
To divide (8x³ - 10x² + 9x-10) ÷ (2x - 1) using long division, follow these steps:
- Start by dividing the first term of the numerator (8x³) by the first term of the denominator (2x).
- Divide 8x³ by 2x to get 4x².
- Multiply the entire denominator (2x - 1) by 4x², and subtract the result from the numerator (8x³ - 10x² + 9x-10).
- Continue the process by dividing the new numerator by the denominator, and repeat until you've gone through all the terms. The final result will be the quotient.
So, (8x³ - 10x² + 9x-10) ÷ (2x - 1) = 4x² + 2x + 11, with a remainder of -21.