Question

Use long division to divide the polynomial. (4x^(3)+8x^(2)-9x+4)-:(2x-1)

Answer 1

To divide the polynomial (4x^3 + 8x^2 - 9x + 4) by (2x - 1) using long division, start by dividing the first term of the numerator by the first term of the denominator. Write the result, multiply it by the denominator to get the partial result, subtract the partial result from the numerator, bring down the next term, and repeat until there are no more terms. Finally, write the quotient and remainder.

Step-by-step explanation:

To divide the polynomial (4x^3 + 8x^2 - 9x + 4) by (2x - 1) using long division, follow these steps:

1. Start by dividing the first term of the numerator (4x^3) by the first term of the denominator (2x).
2. Write the result above the division symbol and multiply it by the denominator to get the partial result.
3. Subtract the partial result from the numerator to get the new numerator.
4. Bring down the next term of the numerator and repeat steps 1-3 until there are no more terms.
5. Write the final quotient and remainder.

By performing long division, the quotient of the division is 2x^2 + 6x + 7 and the remainder is 11.