Question

Divide $3x^3-2x^2+5$ by $x^2-1$

• A. $\frac{3x+4}{x^2-1}$
• B. 3x + $\frac{3x+4}{x^2-1}$
• C. 3x - 2 + $\frac{3x+4}{x^2-1}$
• D. 3x - 2 + $\frac{3x+4}{x-1}$

Answer 1

The correct option is C

3x - 2 + $\frac{3x+4}{x^2-1}$

Step 1: Make sure the polynomial is written in descending order.

Step 2: Divide the term with the highest power inside the division symbol by the term with the highest power outside the division symbol. In this case, we have 3x³ divided by x² which is 3x

Step 3: Multiply (or distribute) the answer obtained in the previous step by the polynomial in front of the division symbol. In this case, we need to multiply 3x and x² – 1.

Step 4: Subtract and bring down the next term.

Step 5: Divide the term with the highest power inside the division symbol by the term with the highest power outside the division symbol. In this case, we have –2x² divided by x² which is –2.

Step 6: Multiply (or distribute) the answer obtained in the previous step by the polynomial in front of the division symbol. In this case, we need to multiply –2 and x² – 1.

Step 7: Subtract and notice there are no more terms to bring down.

Step 8: Write the final answer. The term remaining after the last subtract step is the remainder and must be written as a fraction in the final answer.

Finally we get the answer as 3x - 2 + $\frac{3x+4}{x^2-1}$