How to Divide Polynomials Using Long Division?

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Step-by-step guide to dividing polynomials using long division

A long-division polynomial is an algorithm for dividing a polynomial into another polynomial of the same or lower degree.

The long division of polynomials also consists of a divisor, a quotient, a dividend, and a remainder.

The following are the steps for the long division of polynomials:

• Step 1. Sort the terms in decreasing order of their indices (if needed). Write the missing terms with a coefficient of zero.
• Step 2. For the first term of the quotient, divide the first term of the dividend by the first term of the divisor.
• Step 3. Multiply this quotient statement by the divisor to get the product.
• Step 4. Subtract this product from the dividend and drop the next term (if any). The difference and the brought down term will form the new dividend.
• Step 5. Follow this process until you get a remainder, which can be zero or an index less than the divisor.

Dividing Polynomials Using Long Division – Example 1:

Divide by using long division. \((4x^3-3x^2+4x)\: \div\: (2x+1)\)

Solution:

Therefore, quotient \(=2x-\frac{3}{2}\) and remainder \(= x+\frac{3}{2}\).