There are three common ways of factoring: • factoring by the greatest common monomial factor • factoring following a pattern • factoring by grouping or the box method
Greatest Common Monomial Factor GCF • The greatest common factor or is the greatest integer that is a factor of each of the given integers. • The greatest common monomial factor (GCMF) is the monomial with the numerical coefficient and the greatest that is a factor of each term of the polynomial. • Always look for a greatest common monomial factor first, and then try the other two methods. greatest degree
Factoring by Finding a Pattern • Remember, always look for a GCMF before looking for a pattern. • Perfect Square Trinomial Patterns For all a and b, and • Difference of Squares Pattern (Note: the sum of squares is factorable) For all a and b, not
Factor completely. 3. 4.
Factoring by Finding a Pattern • Sum of Cubes For all a and b, • Difference of Cubes For all a and b,
Factor Completely. 5. 6.
Factoring by Grouping or the Box Method • Factoring a polynomial in the form • Example: • Factor completely . • Draw a 2x2 box:
Place the highest degree term in the top left box and the constant in the bottom right box. • Now, multiply the two together, what do you get?
Find factors of that product that add to the middle term of the trinomial. • *If the product is positive, the factors are either both positive or both negative • *If the product is negative, one factor is positive and one factor is negative.
Place each factor in one of the remaining boxes. • Then, factor out the GCMF from each column and each row. If the top most term or left most term is negative, factor out the negative. If there is no GCMF, factor out a 1. Write your results as two binomials multiplied in parentheses • Use FOIL to check your answer!
Factor completely. 7. 8.
Your Turn! • Factor #9-12
9. 10. 11. 12.