factorising quadratics product method

6x2 + 7x + 2 = ( ?x + ?)( ?x + ? )

6x2 + 7x + 2 Multiply the first and last terms.

6 x 2 = 12

6x2 + 7x + 2

Separate this number into a different pair of factors

Multiply the first and last terms.

6 x 2 = 12

12 x 1 ?

4 x 3 ?

6x2 + 7x + 2 Multiply the first and last terms.

6 x 2 = 12

Choose the pair that add to make the middle term.

12 x 1 ?

4 x 3 ?

Separate this number into a different pair of factors

6x2 + 7x + 2 Multiply the first and last terms.

6 x 2 = 12

Separate the middle term6x2 + 3x + 4x + 2

= 3( 2x2 + x ) + 2( 2x + 1 )

= 3x( 2x + 1 ) + 2( 2x + 1 )

= ( 3x + 2 )( 2x + 1 )

12 x 1 ?

4 x 3 ?

Separate this number into a different pair of factors

6x2 + 7x + 2 Multiply the first and last terms.

6 x 2 = 12

Separate the middle term6x2 + 3x + 4x + 2

= 3( 2x2 + x ) + 2( 2x + 1 )

= 3x( 2x + 1 ) + 2( 2x + 1 )

= ( 3x + 2 )( 2x + 1 )

12 x 1 ?

4 x 3 ?

Separate this number into a different pair of factors

Factorise and regroup

6x2 + 11x + 4 = ( ?x + ? )( ?x + ? )

6x2 + 11x + 4 = ( ?x + ? )( ?x + ? )

24

6x2 + 11x + 4 = ( ?x + ? )( ?x + ? )

24

1 x 24 ?2 x 12 ?3 x 8 ?

6x2 + 11x + 4 = ( ?x + ? )( ?x + ? )

24

1 x 24 ?2 x 12 ?3 x 8 ?

6x2 + 11x + 4 = ( ?x + ? )( ?x + ? ) = 6x2 + 3x + 8x + 4

24

1 x 24 ?2 x 12 ?3 x 8 ?

6x2 + 11x + 4 = ( ?x + ? )( ?x + ? ) = 6x2 + 3x + 8x + 4

24

1 x 24 ?2 x 12 ?3 x 8 ?

= 3x (2x + 1) + 4( 2x + 1 )

= ( 3x + 4 )(2x + 1)

END