Factoring Trinomials of the Type: ax 2 + bx + c Most trinomials can be factored even when the leading coefficient is something other than 1. Examples of trinomials in the form ax 2 + bx + c : 4x 2 + 3x – 182y 2 – 8y – 20 -5c 2 + 7c + 127x 2 – 10x + 16

Factoring Trinomials of the Type: ax 2 + bx + c In order to factor a trinomial, check for a couple conditions: 1) Check for a GCF. Factor it out if one exists. 2) Check to be sure the trinomial is in descending order. After these conditions are met, we are ready to factor. a) Multiply the first coefficient by the last coefficient. b) Find factors of that product that add up to the middle term’s coefficient. c) Make the box like we did for multiplying binomials and break up the middle term using the factors you found in step b. d) Factor each part using GCF. 1 st term Last term Middle term 1 st factor Middle term 2 nd factor

Factoring Trinomials of the Type: ax 2 + bx + c Factor 6x x + 3 Find factors of (3)(6)=18 that add up to , 9 6x 2 3 2x 9x Find the GCF 2x Find the GCF 3 3x1 ( )( ) 2x 3 + 3x 1 +

Factoring Trinomials of the Type: ax 2 + bx + c Factor 9y 2 + 6y − 8 Find factors of (9)(-8)= -72 that add up to , 12 9y y 12y Find the GCF 3y Find the GCF 4 3y-2 ( )( ) 3y4 + 2 −