Factoring Trinomials with a 1 Objective To discover

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 o p m u s bers m u n h t bo e must b. positive 3 x 2 + 11 x + 6 product sum 1 • 18 + 19 2 • 9 + 11 18 + 11

Multiply 3 times – 6. e the To mak ve, siti o p m u s est g r a l e h t ust m r e b num tive. be posi product – 18 3 x 2 + 7 x – 6 sum +7 – 1 • 18 + 17 – 2 • 9 +7

Multiply 3 times – 6. e the To mak ive, gat sum ne est g r a l e h t ust m r e b num tive. a g e n e b product – 18 3 x 2 – 7 x – 6 sum – 7 1 • – 18 – 17 2 • – 9 – 7 Check using the F. O. I. L. method: ( 3 x + 2 ) ( x – 3 ) 3 x 2 – 9 x + 2 x – 6 3 x 2 – 7 x – 6

Multiply 9 times 4. e the To mak ive, gat sum ne bers m both nu e must b e. negativ product 36 9 x 2 – 12 x + 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: ( 3 x – 2 ) 9 x 2 – 6 x + 4 9 x 2 – 12 x + 4

Perfect Square Trinomials

Factoring a Difference of Squares x 2 – 16

4 x 2 – 9 25 x 2 – 49 81 x 2 – 100

ALWAYS check your work.