Question

Divide 3x⁴ - 4x³ - 6x² + 17x - 8 by 3x - 4. Express the result in quotient form. Identify any restrictions on the variable.

Answer 1

To divide the polynomial 3x⁴ - 4x³ - 6x² + 17x - 8 by 3x - 4, you can use long division. The quotient is x³ - 3x² + 3x + 9, and there are no restrictions on the variable x.

Step-by-step explanation:

To divide the polynomial 3x⁴ - 4x³ - 6x² + 17x - 8 by 3x - 4, we can use long division. Here are the steps:

1. First, divide the leading term of the dividend, 3x⁴, by the leading term of the divisor, 3x.
2. This gives us x³ as the first term of the quotient.
3. Next, multiply the divisor, 3x - 4, by the x³ term of the quotient and subtract the result from the dividend.
4. Repeat the process with the new dividend until all terms have been divided.
5. The final quotient is x³ - 3x² + 3x + 9.

There are no restrictions on the variable x in this division problem. The quotient is valid for all values of x.