Here are the steps required for Dividing by a Polynomial Containing More Than One Term (Long Division):

 Step 1: Make sure the polynomial is written in descending order. If any terms are missing, use a zero to fill in the missing term (this will help with the spacing). Step 2: Divide the term with the highest power inside the division symbol by the term with the highest power outside the division symbol. Step 3: Multiply (or distribute) the answer obtained in the previous step by the polynomial in front of the division symbol. Step 4: Subtract and bring down the next term. Step 5: Repeat Steps 2, 3, and 4 until there are no more terms to bring down. Step 6: 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.

Example 1 – Divide: Step 1: Make sure the polynomial is written in descending order. If any terms are missing, use a zero to fill in the missing term (this will help with the spacing). In this case, the problem is ready as is. 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 x3 divided by x which is x2. 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 x2 and x + 2. 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 –6x2 divided by x which is –6x. 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 –6x and x + 2. Step 7: Subtract and bring down the next term. Step 8: 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 14x divided by x which is +14. Step 9: 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 14 and x + 2. Step 10: Subtract and notice there are no more terms to bring down. Step 11: 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. Example 2 – Divide: Step 1: Make sure the polynomial is written in descending order. If any terms are missing, use a zero to fill in the missing term (this will help with the spacing). In this case, we should get: 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 4x3 divided by x2 which is 4x. 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 4x and x2 + 3x – 2. 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 –25x2 divided by x2 which is –25. 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 –25 and x2 + 3x – 2. 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. Example 3 – Divide: Step 1: Make sure the polynomial is written in descending order. If any terms are missing, use a zero to fill in the missing term (this will help with the spacing). In this case, we should get: 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. Example 4 – Divide: Step 1: Make sure the polynomial is written in descending order. If any terms are missing, use a zero to fill in the missing term (this will help with the spacing). In this case, we should get: Steps 2, 3, and 4: Divide the term with the highest power inside the division symbol by the term with the highest power outside the division symbol. Next multiply (or distribute) the answer obtained in the previous step by the polynomial in front of the division symbol. In this case, we should get 2x3/2x = x2 and x2(2x + 3). Finally, subtract and bring down the next term. Steps 5, 6, and 7: Divide the term with the highest power inside the division symbol by the term with the highest power outside the division symbol. Next multiply (or distribute) the answer obtained in the previous step by the polynomial in front of the division symbol. In this case, we should get 4x2/2x = 2x and 2x(2x + 3). Finally, subtract and bring down the next term. Steps 8, 9, and 10: Divide the term with the highest power inside the division symbol by the term with the highest power outside the division symbol. Next multiply (or distribute) the answer obtained in the previous step by the polynomial in front of the division symbol. In this case, we should get –4x/2x = –2 and –2(2x + 3). Finally, subtract and notice there are no more terms to bring down. Step 11: 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. Example 5 – Divide: Step 1: Make sure the polynomial is written in descending order. If any terms are missing, use a zero to fill in the missing term (this will help with the spacing). In this case, the problem is ready as is. Steps 2, 3, and 4: Divide the term with the highest power inside the division symbol by the term with the highest power outside the division symbol. Next multiply (or distribute) the answer obtained in the previous step by the polynomial in front of the division symbol. In this case, we should get x3/x2 = x and x(x2 + x – 6). Finally, subtract and bring down the next term. Steps 5, 6, and 7: Divide the term with the highest power inside the division symbol by the term with the highest power outside the division symbol. Next multiply (or distribute) the answer obtained in the previous step by the polynomial in front of the division symbol. In this case, we should get 2x2/x2 = 2 and 2(x2 + x – 6). Finally, 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. In this case, there is no remainder, so you do not need to write the fraction. 