1. HIGH SCHOOL MATH FACTORING

2. Ask Yourself the following questions… FACTORINGFACTORING 1Is there a common factor? Example: 6x 2 + 8x = 2x 1. What is the common factor? 2. Remove the common factor. 3. Divide each elements of the expression by the common factor. ( ) ( 3x + 4 ) = 2x

3. Ask Yourself the following questions… FACTORINGFACTORING 2 Is there the difference between two squares? Example: 4x 2 – 81 =(2x 9 ) ( 2x 9 ) =( ) ( ) How to determine if something is a “Difference of Two Squares” 1. Is the first term a perfect square? 2. Is the second term a perfect square? 3. Is there a negative sign in the middle? Then the expression is a Difference of Two Squares” 1. Use the Two Factor Method 2. Take the square root of the 1 st and the square root of the 2 nd 3. Use opposite signs in the middle =(2x + 9 ) ( 2x - 9 )

4. Ask Yourself the following questions… FACTORINGFACTORING 3Is there a perfect square? Example: x 2 + 8x + 16 How to determine if something is a “Perfect Square” 1.Is the first term a perfect square? 2.Is the last term a perfect square? 3.Recall: ax 2 + bx + c = 0 4.Does ( ½ b ) 2 = c ? Then the expression is a Perfect Square” 1.Set up the factor 2.Take the square root of the 1 st term and the square root of the last term 3. Use the sing of the middle term and place it between the square roots = ( ) 2 = ( x 4 ) 2 = ( x + 4 ) 2

5. Ask Yourself the following questions… FACTORINGFACTORING 4Is the coefficient of the x 2 ’d term = 1? Example: = ( ) ( ) x 2 – 7x + 10 1. Use the two factor method 2. Factor the 1 st term of the expression 3. Determine the signs of the factors 4. Determine the values of the2 nd term = ( x ) ( x ) = ( x - ) ( x - ) To determine the Signs of the Factors Recall: ax 2 + bx + c = 0 1. Consider the sign of the “c” term 2. If the sign is + then both signs will be the SAME and the factors will both have the sign of the “b” term 3. If the sign is – then both signs will be DIFFERENT and the higher number will take the sign of the “b” term To determine the Values of the Second Term Recall: ax 2 + bx + c = 0 1.What two numbers multiplied together will give the “c” term * = c 2. What same two numbers will give the “b” term + = b = ( x - 5 ) ( x - 2 )

6. Ask Yourself the following questions… FACTORINGFACTORING 5Is the coefficient of the x 2 ‘ d term ≠ 1 Example: 6x 2 + 5x - 4 1. Factor by “Grouping” = 6x 2 +5x - 4 = 6x 2 + 8x – 3x - 4 Recall ! 6x 2 + 5x – 4 1.The signs will be different 2.The larger number will be + Recall ! 6x 2 + 5x – 4 1. What 2 # ’ s multiplied together will give (6 * -4), -24 ? 2. What same 2 # ’ s added together will give 5 ? = 2x (3x + 4 ) – 1 (3x + 4) = (3x + 4 ) (2x - 1) 2. Determine the factors of the middle term 4. Remove the binomial Common Factor 3. Remove the common factor from the 2 groups

7. FACTORINGFACTORING

8. 1 2 3 5 4 Is there a common factor? Is there the difference of two squares? Is there a perfect square? Is the coefficient of the x 2 ’d term = 1? Is the coefficient of the x 2 ’d term ≠ 1?