Question

Use long division to fine the quotient (4x^3-6x^2-4x+8) divided by (2x)

Answer 1

The quotient of (4x^3-6x^2-4x+8) divided by (2x) is 2x^2 + x - 2.

Step-by-step explanation:

To divide (4x^3-6x^2-4x+8) by (2x) using long division, follow these steps:

1. Start by dividing the first term, 4x^3, by 2x. The quotient is 2x^2.
2. Multiply 2x by (2x), which is 4x^2, and subtract it from the original polynomial. Now you have -6x^2 - 4x + 8 - 4x^2 = 2x^2 - 4x + 8.
3. Next, divide the new polynomial, 2x^2 - 4x + 8, by 2x. The quotient is x - 2.
4. Multiply 2x by (x - 2), which is 2x^2 - 4x, and subtract it from the new polynomial. Now you have -4x + 8 - (2x^2 - 4x) = -2x^2 + 8.
5. Finally, divide the remaining polynomial, -2x^2 + 8, by 2x. The quotient is -x + 4.

Therefore, the quotient of (4x^3-6x^2-4x+8) divided by (2x) is 2x^2 + x - 2.