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Division of polynomials
Division of polynomials. What means to divide one polynomial P by another Q ? It means to find polynomials M ( quotient ) and N ( remainder ), satisfying the two requirements:

1). An equality MQ + N = P takes place;
2). A degree of polynomial N is less than a degree of polynomial Q .

Division of polynomials can be done by the following scheme ( long division ):
1) Divide the first term 16a3 of the dividend by the first term 4a2 of the divisor; the result 4a is the first term of the quotient.

2) Multiply the received term 4a by the divisor 4a2a + 2; write the result 16a3 – 4a2 + 8a under the dividend, one similar term under another.

3) Subtract terms of the result from the corresponding terms of the dividend and move down the next by the order term 7 of the dividend; the remainder is 12a2 – 13a + 7 .

4) Divide the first term 12a2 of this expression by the first term 4a2 of the divisor; the result 3 is the second term of the quotient.

5) Multiply the received second term 3 by the divisor 4a2a + 2; write the result 12a2 – 3a + 6 again under the dividend, one similar term under another.

6) Subtract terms of the result from the corresponding terms of the previous remainder and receive the second remainder: – 10a + 1. Its degree is less than the divisor degree, therefore the division has been finished. The quotient is 4a + 3, the remainder is – 10a + 1.
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