Question

What is the result when 18x^(3)+12x^(2)+15x-7 is divided by 3x-1?

Answer 1

To divide 18x^(3)+12x^(2)+15x-7 by 3x-1, you can use polynomial long division. The result is 6x^2+5x+6.

Step-by-step explanation:

To divide 18x^(3)+12x^(2)+15x-7 by 3x-1, you can use polynomial long division. Here are the steps:

1. Divide the first term of the dividend (18x^3) by the first term of the divisor (3x). The result is 6x^2.
2. Multiply the entire divisor (3x-1) by the quotient obtained in step 1 (6x^2) and subtract it from the dividend (18x^3+12x^2+15x-7).
3. The subtraction in step 2 will give you a new dividend. Repeat steps 1 and 2 until you can no longer divide.
4. The final result of the division is the quotient plus any remainder. In this case, the quotient is 6x^2+5x+6 and there is no remainder.

Therefore, when 18x^3+12x^2+15x-7 is divided by 3x-1, the result is 6x^2+5x+6.