 # When to stop dividing in the long division of polynomials. Lipossig 2020-12-09 Answered
When to stop dividing in the long division of polynomials.
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When a divisor has more than one term or if the divisor is a polynomial containing more than one term, the four steps used to divide whole numbers— (divide, multiply, subtract, bring down the next term)—form the repetitive procedure for the polynomial long division.
Below is a list of steps that can be followed for dividing by a polynomial(A long division of polynomials):
Step 1: Arrange the terms of both the dividend and the divisor in descending powers of any variable.
Step 2: Divide the first term in the dividend by the first term in the divisor. The result is the first term of the quotient.
Step 3: Multiply every term in the divisor by the first term in the quotient, Write the resulting product beneath the dividend with like terms lined up.
Step 4: Subtract the product from the dividend.
Step 5: Bring down the next term in the original dividend and write it next to the remainder to form a new dividend.
Step 6: Use this new expression as the dividend and repeat this process until the remainder can no longer be divided. This will occur when the degree of the remainder (the highest exponent on a variable in the remainder) is less than the degree of the divisor.
Example: $$divisor = x^{2} + 1$$,$$Remainder\ = x + 5$$
Here, the degree of the remainder is “one” which is less than the degree of the divisor, which is “two”. The division should stop at this point as remainder cannot be divided further.