Factoring Trinomials

Factor x2 + 9x + 20

x2 + 9x + 20 ( + )( + ) 5 4 x x Find 2 numbers with a product of 20, and can be combined by addition to equal 9 1 x 20 2 x 10 4 x 5

Check with FOIL ( x + 5)(x + 4) x2 + 4x + 5x + 20 x2 + 9x + 20

x2 + 8x + 16 ( + )( + ) 4 4 x x Find 2 numbers with a product of 16, and can be combined by addition to equal 8 1 x 16 2 x 8 4 x 4

Check with FOIL ( x + 4)(x + 4) x2 + 4x + 4x + 16 x2 + 8x + 16

The – means that one sign will be negative and one will be positive x2 + 2x - 3 - ( )( ) 1 + 3 x x The – means that one sign will be negative and one will be positive Find 2 numbers with a product of 3, and can be combined by addition to equal 2 1 x 3

Check with FOIL ( x - 1)(x + 3) x2 + 3x + -x + -3 x2 + 2x - 3

The – means that one sign will be negative and one will be positive x2 + x - 12 - ( )( ) 3 + 4 x x The – means that one sign will be negative and one will be positive Find 2 numbers with a product of 12, and can be combined by addition to equal 1 1 x 12 2 x 6 3 x 4

Check with FOIL ( x - 3)(x + 4) x2 + 4x + -3x + -12 x2 + x - 12

The – means that one sign will be negative and one will be positive x2 - 2x - 8 - ( )( ) 4 + 2 x x The – means that one sign will be negative and one will be positive Find 2 numbers with a product of 8, and can be combined by addition to equal 2 1 x 8 2 x 4

Check with FOIL ( x - 4)(x + 2) x2 + 2x + -4x + -8 x2 - 2x - 8

x2 - 6x + 9 - ( )( ) 3 - 3 x x The + in front of the 9 and the – in front of the 6 means that both signs will be negative Find 2 numbers with a product of 9, and can be combined by addition to equal 6 1 x 9 3 x 3

Check with FOIL ( x - 3)(x - 3) x2 + -3x + -3x + 9 x2 - 6x + 9

x2 - 7x + 10 - ( )( ) 2 - 5 x x The + in front of the 10 and the – in front of the 7 means that both signs will be negative Find 2 numbers with a product of 10, and can be combined by addition to equal 7 1 x 10 2 x 5

Check with FOIL ( x - 2)(x - 5) x2 + -5x + -2x + 10 x2 - 7x + 10