Question 6 (2x^3-21x^2-4x+16)/(2x-1)

To solve the given expression, we need to perform polynomial long division. Let's divide the numerator by the denominator step by step:1. Divide the leading term of the numerator (2x^3) by the leading term of the denominator (2x). This gives us x^2.2. Multiply x^2 by the entire denominator (2x - 1) to get 2x^3 - x^2.3. Subtract this result from the numerator to get -21x^2 - 4x + 16.4. Repeat steps 1-3 with the new numerator. Divide -21x^2 by 2x to get -10.5x.5. Multiply -10.5x by the entire denominator to get -21x^2 + 10.5x.6. Subtract this result from the new numerator to get -14.5x + 16.7. Repeat steps 1-3 with the new numerator. Divide -14.5x by 2x to get -7.25.8. Multiply -7.25 by the entire denominator to get -14.5x + 7.25.9. Subtract this result from the new numerator to get 8.75.Therefore, the simplified expression is: