1. Factoring Trinomials with a > 1 Factor trinomials when the coefficient of x 2 is a number greater than 1. ax 2 + bx + c

2. 3x 2 + 11x + 6 18 + 11 1 18 2 9 Multiply 3 times 6. product sum To make the sum positive, both numbers must be positive. Use the coefficient of x 2 in both parentheses: ( 3x ) ( 3x ) Fill in the numbers… ( 3x + 2 ) ( 3x + 9 ) Factor any common terms from each parenthesis. ( 3x + 2 ) ( 3x + 9 ) 1 3 ( 3x + 2 ) ( x + 3 ) + 19 + 11 Check using the F.O.I.L. method: ( 3x + 2 ) ( x + 3 ) 3x 2 + 9x + 2x + 6 3x 2 + 11x + 6

3. 3x 2 + 7x – 6 –18 + 7 –1 18 –2 9 Multiply 3 times – 6. product sum To make the sum positive, the largest number must be positive. Use the coefficient of x 2 in both parentheses: ( 3x ) ( 3x ) Fill in the numbers… ( 3x – 2 ) ( 3x + 9 ) Factor any common terms from each parenthesis. ( 3x – 2 ) ( 3x + 9 ) 1 3 ( 3x – 2 ) ( x + 3 ) + 17 + 7 Check using the F.O.I.L. method: ( 3x – 2 ) ( x + 3 ) 3x 2 + 9x – 2x – 6 3x 2 + 7x – 6

4. 3x 2 – 7x – 6 –18 – 7 1 –18 2 – 9 Multiply 3 times – 6. product sum To make the sum negative, the largest number must be negative. Use the coefficient of x 2 in both parentheses: ( 3x ) ( 3x ) Fill in the numbers… ( 3x + 2 ) ( 3x – 9 ) Factor any common terms from each parenthesis. ( 3x + 2 ) ( 3x – 9 ) 1 3 ( 3x + 2 ) ( x – 3 ) – 17 – 7 Check using the F.O.I.L. method: ( 3x + 2 ) ( x – 3 ) 3x 2 – 9x + 2x – 6 3x 2 – 7x – 6

5. 9x 2 – 12x + 4 36 – 12 –1 –36 –2 –18 –3 –12 –4 –9 –6 Multiply 9 times 4. product sum To make the sum negative, both numbers must be negative. Use the coefficient of x 2 in both parentheses: ( 9x ) ( 9x ) Fill in the numbers… ( 9x – 6 ) ( 9x – 6 ) Factor any common terms from each parenthesis. ( 9x – 6 ) ( 9x – 6 ) 3 ( 3x – 2 ) – 37 – 20 Check using the F.O.I.L. method: ( 3x – 2 ) 9x 2 – 6x – 6x + 4 9x 2 – 12x + 4 – 15 – 13 – 12 ( 3x – 2 ) 2

6. 4x 2 – 9 – 36 0 1 – 36 6 – 6 Multiply – 9 times 4. product sum To make the sum zero, both numbers must be the same but opposite signs. Use the coefficient of x 2 in both parentheses: ( 4x ) ( 4x ) Fill in the numbers… ( 4x + 6 ) ( 4x – 6 ) Factor any common terms from each parenthesis. ( 4x + 6 ) ( 4x – 6 ) 2 ( 2x + 3 ) ( 2x – 3 ) – 35 0 Check using the F.O.I.L. method: ( 2x + 3 ) ( 2x – 3 ) 4x 2 – 6x + 6x – 9 4x 2 – 9

7. ALWAYS check your work when factoring trinomials by using the FOIL method.