Factoring Trinomials.

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Presentation transcript:

Factoring Trinomials

(x + 5)(x + 4) x2 + 9x + 20 5 + 4 5 x 4

Factoring is doing the opposite of FOIL Factor x2 + 9x + 20 Factoring is doing the opposite of FOIL

x2 + 9x + 20 We know we want to end up with 2 binomials ( )( ) +4 +5 x x Find 2 numbers with a product of 20 1 x 20 2 x 10 4 x 5 That can be combined by addition to equal 9

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

x2 + 8x + 16 We know we want to end up with 2 binomials ( )( ) +4 +4 x x Find 2 numbers with a product of 16 1 x 16 2 x 8 4 x 4 That can be combined by addition to equal 8

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

x2 + 2x - 3 - We know we want to end up with 2 binomials + ( )( ) 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 1 x 3 That can be combined by addition to equal +2

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

- x2 + x -12 We know we want to end up with 2 binomials + ( )( ) 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 1 x 12 2 x 6 3 x 4 That can be combined by addition to equal +1

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

x2 - 2x - 8 - - We know we want to end up with 2 binomials + + ( )( ) 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 1 x 8 2 x 4 That can be combined by addition to equal -2

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

x2 - 6x + 9 - We know we want to end up with 2 binomials + ( )( ) 3 3 x - x - The +9 and -6 means that both signs will be negative Find 2 numbers with a product of 9 1 x 9 3 x 3 That can be combined by addition to equal -6

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

x2 - 7x + 10 - We know we want to end up with 2 binomials + ( )( ) 2 5 x - x - The +10 and -7 means that both signs will be negative Find 2 numbers with a product of 10 1 x 10 2 x 5 That can be combined by addition to equal -7

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