1. Polynomials and Polynomial Functions
Chapter 5
Polynomials and Polynomial Functions

2. Chapter Sections 5.1 – Addition and Subtraction of Polynomials
5.2 – Multiplication of Polynomials
5.3 – Division of Polynomials and Synthetic Division
5.4 – Factoring a Monomial from a Polynomial and Factoring by Grouping
5.5 – Factoring Trinomials
5.6 – Special Factoring Formulas
5.7-A General Review of Factoring
5.8- Polynomial Equations
Chapter 1 Outline

3. A General Review of Factoring
§ 5.7
A General Review of Factoring

4. To Factor a Polynomial
1. Determine whether all the terms in the polynomial have a GCF other than 1. If so, factor out the GCF.
2. If the polynomial has two terms, determine whether it is a difference of two squares or a sum or difference of two cubes. If so, factor using the appropriate formula from Section 5.6.
3. If the polynomial has three terms, determine whether it is a perfect square trinomial. If so, factor accordingly. If it is not, factor the trinomial using trial and error, grouping, or substitution as explained in Section 5.5.

5. To Factor a Polynomial
4. If the polynomial has more than three terms, try factoring by grouping. If that does not work, see if three of the terms are the square of a binomial.
5. As a final step, examine your factored polynomial to see if any factors listed have a common factor and can be factored further. If you find a common factor, factor it out at this point.
6. Check the answer by multiplying the factors.

6. Examples Example: a.) Factor 2x4 – 50x2.
First, check for a greatest common factor other than 1. Since 2x2 is common to both terms, factor it out.

7. Examples Example: c.) Factor 24x2 – 6xy + 40xy – 10y2
In this example, 2 is common to all terms. Factor out the 2; then factor the remaining four-term polynomial by grouping.

8. Examples Example: e.) Factor 3x2 – 18x + 27 – 3y2.
Factor out 3 from all four terms.
Now try factoring by grouping.