what is division algorithm for polynomial Related: Important definitions and formulas - Polynomials?

Question

what is division algorithm for polynomial Related:  Important definitions and formulas - Polynomials?

Answer

Division algorithm for polynomials states that, suppose f(x) and g(x) are the two polynomials, where g(x)≠0, we can write: f(x) = q(x) g(x) + r(x) which is same as the Dividend = Divisor * Quotient + Remainder and where r(x) is the remainder polynomial and is equal to 0 and degree r(x) < degree='' g(x).='' degree='' />

Answer

Answer

Division Algorithm for Polynomials:
The division algorithm for polynomials is a process used to divide one polynomial by another. It is similar to long division for numbers but involves dividing polynomials instead. Here is how the division algorithm for polynomials works:

Step 1: Divide the leading term of the dividend by the leading term of the divisor
- Start by dividing the leading term of the dividend by the leading term of the divisor. This will give you the first term of the quotient.

Step 2: Multiply the entire divisor by the first term of the quotient
- Multiply the entire divisor by the first term of the quotient and subtract the result from the dividend.

Step 3: Repeat the process
- Repeat the process by dividing the leading term of the new dividend by the leading term of the divisor. This will give you the next term of the quotient. Multiply the entire divisor by this term and subtract from the dividend. Continue this process until you can no longer divide.

Step 4: Write the final quotient and remainder
- Write the final quotient as the sum of all the terms obtained during the division process. The remaining terms after division represent the remainder.
By following these steps, you can successfully divide one polynomial by another using the division algorithm.

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