Chapter 7    Factoring

1.  Finding prime factors- 

     Factors of   48 =  (1)(48) = (2)(24)=(16)(3) = (4)(12) = (4)(4)(3); prime factors- (2⁴)(3)

     Finding the greatest common factor and factoring out- Ex.  4a² -20a = 4a(a -5)

     Factoring by grouping

2. Factoring trinomials-  Ex     x² + 3x + 2 can be factored as (x +2)(x+1) check it by FOIL to see whether it    

    gives the original expression.

3. Special factorizations-  Difference between two squares    a² - b²   =  (a + b)(a - b) 

                                                                                    a² + 2ab + b² =  (a + b)²

                                                                                    a² - 2ab + b² =  (a - b)²

4. Solving quadratic equations by factoring:

    Ex.   To solve  x² -3x + 2 = 0

            Find factors   (x - 2)(x - 1) = 0; therefore  x - 2 = 0  and/or x - 1 = 0

            Giving x = 2 or x = 1 as the solutions

5. Applications of quadratic equations