Question

Divide the following: (6x^3 - 23x^2 + 23x - 5) / (3x - 4).

Answer 1

To divide the given polynomial (6x^3 - 23x^2 + 23x - 5) by the polynomial (3x - 4), you can use polynomial long division technique. The quotient obtained after the process is 2x^2 - 5x + 3.

Step-by-step explanation:

To divide the given polynomial (6x^3 - 23x^2 + 23x - 5) by the polynomial (3x - 4), you can use polynomial long division. Here's how:

1. Start by dividing the leading term of the numerator (6x^3) by the leading term of the denominator (3x). This gives you 2x^2.
2. Multiply the entire denominator (3x - 4) by the quotient you just found (2x^2). This gives you 6x^3 - 8x^2.
3. Subtract this product from the original numerator: (6x^3 - 23x^2 + 23x - 5) - (6x^3 - 8x^2). Simplify to get -15x^2 + 23x - 5.
4. Now, repeat the process with the new numerator (-15x^2 + 23x - 5) and the denominator (3x - 4). You will find that the quotient is -5x + 3.
5. There is no remainder, so the final result is the quotient: 2x^2 - 5x + 3.