How do you divide polynomials examples?

Dividing Polynomials

Example: Evaluate (x2 + 8x) ÷ x.
Solution: (x2 + 8x) ÷ x. = [x2 ÷ x] + [8x ÷ x] = x + 8.
Example: Evaluate (4y4 – y3 + 2y2) ÷ (–y2)
Solution: (4y4– y3 + 2y2) ÷ (–y2) = [4y4 ÷ –y2] + [– y3 ÷ –y2] + [2y2 ÷ –y2] = –4y2 + y – 2.

What is the easiest way to divide polynomials?

How To: Given two polynomials, use synthetic division to divide

Write k for the divisor.
Write the coefficients of the dividend.
Bring the leading coefficient down.
Multiply the leading coefficient by k.
Add the terms of the second column.
Multiply the result by k.
Repeat steps 5 and 6 for the remaining columns.

Why do we divide polynomials?

Thus long division is a means for testing whether one polynomial has another as a factor, and, if it does, for factoring it out. For example, if a root r of A is known, it can be factored out by dividing A by (x – r).

Is a polynomial divided by a polynomial always a polynomial?

There is no guarantee that a quotient of polynomials can be expressed as a polynomial, even though it sometimes can. As a simple example, note that both the numerator and denominator of 1x are polynomials, albeit trivial ones. Yet, this quotient is equivalent to x−1, which we know is not a polynomial.

Is a polynomial multiplied by a polynomial a polynomial?

True: the product of two polynomials will be a polynomial regardless of the signs of the leading coefficients of the polynomials. When two polynomials are multiplied, each term of the first polynomial is multiplied by each term of the second polynomial.

How do you divide two polynomials?

There are two ways to divide polynomials. One is to write the division in rational form, factor the polynomials, and then cancel out any common factors: Divide x 2 + 9x + 14 by x + 7. Another option for dividing polynomials is to apply the process of long division.

What are the rules for dividing polynomials?

To divide two polynomials, here are the procedures: Arrange both the divisor and dividend in descending order of their degrees. Divide the 1 st term of the dividend by the 1 st term of the divisor to obtain the 1 st term of the quotient. Find the product of all the terms of the divisor and the 1 st term quotient and subtract the dividend’s answer.

What is long division of polynomials?

Polynomial long division. In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division.