Polynomials and Polynomial Functions Chapter 5 Polynomials and Polynomial Functions

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

A General Review of Factoring § 5.7 A General Review of Factoring

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.

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.

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.

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.

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