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##### HIGH SCHOOL MATH

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**HIGH SCHOOL MATH**FACTORING**Ask Yourself the following questions…**1 Is there a common factor? Example: F A C T O R I N G = 2x ( ) ( 3x + 4 ) = 2x 1. What is the common factor? 2. Remove the common factor. 3. Divide each elements of the expression by the common factor.**Ask Yourself the following questions…**Is there the difference between two squares? 2 Example: F A C T O R I N G 4x2 – 81 = ( ) ( ) 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” =(2x 9 ) ( 2x 9 ) =(2x + 9 ) ( 2x - 9 ) 1. Use the Two Factor Method 2. Take the square root of the 1st and the square root of the 2nd 3. Use opposite signs in the middle**Ask Yourself the following questions…**3 Is there a perfect square? Example: F A C T O R I N G x2 + 8x + 16 = ( )2 • How to determine if something is a “Perfect Square” • Is the first term a perfect square? • Is the last term a perfect square? • Recall: ax2 + bx + c = 0 • Does ( ½ b )2 = c ? • Then the expression is a Perfect Square” = ( x 4 )2 = ( x + 4 )2 • Set up the factor • Take the square root of the 1st term and the square root of the last term 3. Use the sing of the middle term and place it between the square roots**To determine the Signs of the Factors**Recall: ax2 + 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: ax2 + bx + c = 0 • What two numbers multiplied together will give the “c” term • * = c • 2. What same two numbers will give the “b” term • + = b Ask Yourself the following questions… 4 Is the coefficient of the x2’d term = 1? Example: F A C T O R I N G x2 – 7x + 10 = ( ) ( ) = ( x ) ( x ) = ( x - ) ( x - ) = ( x - 5 ) ( x - 2 ) 1. Use the two factor method 2. Factor the 1st term of the expression 3. Determine the signs of the factors 4. Determine the values of the2nd term**Recall !**• 6x2 + 5x – 4 • The signs will be different • The larger number will be + Recall ! 6x2 + 5x – 4 1. What 2 # ’ s multiplied together will give (6 * -4), -24 ? 2. What same 2 # ’ s added together will give 5 ? Ask Yourself the following questions… 5 Is the coefficient of the x2 ‘d term ≠ 1 Example: 6x2 + 5x - 4 F A C T O R I N G = 6x2 +5x - 4 = 6x2 + 8x – 3x - 4 = 2x (3x + 4 ) – 1 (3x + 4) = (3x + 4 ) (2x - 1) 1. Factor by “Grouping” 2. Determine the factors of the middle term 3. Remove the common factor from the 2 groups 4. Remove the binomial Common Factor**LET'S**REVIEW F A C T O R I N G**Ask yourself the following questions...**1 Is there a common factor? 2 Is there the difference of two squares? 3 Is there a perfect square? 4 Is the coefficient of the x2’d term = 1? 5 Is the coefficient of the x2’d term ≠ 1?