7.9+Dividing+Polynomials

Section 7.9 - Dividing Polynomials
We will cover only the simplest process of dividing polynomials - dividing by a monomial, or single term.

When you divide a polynomial by a monomial, you are actually dividing each term in the polynomial by the monomial. The picture below shows how that is done theoretically, though you probably would just do this step in your mind as you solve this kind of problem.



When you view it this way, you can simply reduce each fraction by dividing the coefficients and the variables. You might also see that the Quotient Rule of Exponents comes into play here.




 * Factoring Out a Common Factor**

Sometimes you are given a polynomial and asked to factor out the greatest common factor. You will need to find the single term that evenly "goes into" each of the terms in the polynomial. The solution is to think of each term as a product of factors (numbers and variables). Then just find the minimum number of times that each factor goes into each of the terms and multiply those back together.



If we start with the coefficients, you can see that 5 is a factor of each of the three terms (35, 20, and -10). A is a factor in each term, but there are 3 a's in the first term, 4 in the second, and 2 in the last, so a squared is the greatest factor in each. B is a factor in the first two terms, but not the last, so it can't be in the common factor. C is in all terms, but there is only one in the first term, so C is the only common factor.

The answer, then, is:


 * Note**: If the first term in the polynomial is negative, include the negative sign with the factor that you pull out (in the example above, the coefficient of 5 would be negative 5 instead).

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 * Chapter Seven Practice Problems**

**Where to from here?**
7.1 Negative Exponents 7.2 Product Rule 7.3 Power Rule 7.4 Quotient Rule 7.5 Defining Polynomials 7.6 Adding Polynomials 7.7 Subtracting Polynomials 7.8 Multiplying Polynomials 7.9 Dividing Polynomials Chapter Seven Summary Chapter Seven Homework