Question

Use long division. (27x³+9x²-3x-10)-:(3x-2)

Answer 1

To divide (27x³+9x²-3x-10) by (3x-2) using long division, divide the first term of the numerator by the first term of the denominator, subtract the product from the numerator, and repeat the process with the new numerator until you have no more terms to divide.

Step-by-step explanation:

To divide (27x³+9x²-3x-10) by (3x-2) using long division, follow these steps:

1. Start by dividing the first term of the numerator, 27x³, by the first term of the denominator, 3x. This gives you 9x².
2. Multiply (3x-2) by 9x² to obtain 27x³-18x².
3. Subtract this product from the numerator (27x³+9x²-3x-10) to get -27x²-3x-10.
4. Repeat the process with this new numerator (-27x²-3x-10): divide the first term (-27x²) by the first term of the denominator (3x) to get -9x. Multiply (3x-2) by -9x to obtain -27x²+18x.
5. Subtract this product from the current numerator (-27x²-3x-10) to get -21x-10.
6. Finally, divide the remaining numerator (-21x-10) by the first term of the denominator (3x) to get -7. Multiply (3x-2) by -7 to obtain -21x+14.
7. Subtract this product from the current numerator (-21x-10) to get -24.

Therefore, the quotient when dividing (27x³+9x²-3x-10) by (3x-2) is 9x²-9x-7 with a remainder of -24.