# Factoring Trinomials with a > 1 Factoring Trinomials with a > 1 Objective: To discover factoring quadratics with a leading coefficient greater than 1 and special care quadratics ax 2 + bx + c Factoring when |a|1 Step 1: Since there is no common factors find ac Step 2: Rewrite bx as the sum of the two terms with coefficients that are factors of ac, and have a sum of b Step 3: Factor Multiply 3 times 6. e the To mak ve,

siti sum po bers m u n h t bo e must b . positive 3x 2 + 11x + 6 product sum

1 18 + 19 29 + 11 18 + 11 Multiply 3 times 6. e the To mak ve, siti sum po st

e the larg st r mu e b m u n tive. i s o p e b product 18

3x 2 + 7x 6 sum +7 1 18 + 17 2 9 +7 Multiply 3 times 6. e the To mak ive, g at

sum ne est g r a l e th ust m r e b num tive. a g e n

e b product 18 3x 2 7x 6 sum 7 1 18 17 29 7 Check using the F.O.I.L. method: ( 3x + 2 ) ( x 3 )

3x 2 9x + 2x 6 3x 2 7x 6 Multiply 9 times 4. e the To mak ive, g at sum ne bers m both nu e must b e. negativ product 36 9x 2 12x + 4

sum 12 1 36 37 2 18 20 3 12 15 4 9 13 6 6 12 Check using the F.O.I.L. method: ( 3x 2 ) ( 3x 2 ) 9x 2 6x 6x + 4 9x 2 12x + 4

Perfect Square Trinomials Factoring a Difference of Squares x 2 16 4x 2 9 25x 2 49 81x 2 100 ALWAYS check your work.