Long Division Of Polynomials
In algebra, long division of Polynomials is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division of Polynomials or Division Algorithm for polynomials. Division algorithm for polynomials can be done easily by hand, because it separates an otherwise complex division problem into smaller ones.Division algorithm for polynomials is similar to long division of whole number,when you divide two polynomials you can check the answer using the following :Dividend = Quotient Ñ… Divisor + Remainder
If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that p(x) = g(x) × q(x) + r(x),where r(x) = 0 or degree of r(x) < degree of g(x).
This result is known as the Division Algorithm for polynomials or long division of Polynomials.
Steps in dividing polynomials using the long division algorithm for polynomials:
- Arrange the indices of the polynomial in descending order.
- Replace the missing term(s) with 0.
- Divide the first term of the dividend (the polynomial to be divided) by the first term of the divisor.
- Multiply the divisor by the first term of the quotient.
- Subtract the product from the dividend then bring down the next term. The difference and the next term will be the new dividend.
- Note: Remember the rule in subtraction "change the sign of the subtrahend then proceed to addition".
- Repeat step 2 – 4 to find the second term of the quotient.
- Continue the process until a remainder is obtained. This can be zero or is of lower index than the divisor.
Lets solve one more question on polynomial-long-division to understand the topic:
Check:
| (x+2) | (x+1) | + | -4 | = | x2 + 3x - 2 |
|---|---|---|---|---|---|
| Quotient | divisor | remainder | dividend |
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