Factorising quadratics

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Factorising quadratics 6x2 + x - 2 is in the form ax2 + bx + c So a = 6, b = 1, c = -2 You need to find 2 numbers which multiply to give ac (in this case -12) and add to give b (in this case +1) Now list the factors of ac

1 -12 -1 12 2 -6 -2 6 3 -4 -3 4 -3 4 Decide which pair adds up to b ie +1 Replace the x term by these two values ie -3x and 4x so 6x2 + x – 2 becomes 6x2 + 4x -3x -2 Now factorise it as a four term expression

6x2 + 4x -3x -2 = 2x (3x + 2) +1 (-3x - 2) There is nothing common in the second part so take out +1 Unfortunately, the signs in the second bracket are – those in the first bracket So instead of taking out +1 we take out -1 = 2x (3x + 2) -1 (3x + 2) The brackets are now the same so take them out as common factors So 6x2 + x - 2= ( 3x + 2 ) ( 2x -1 )

6x2 + 4x -3x -2 = 2x (3x + 2) +1 (-3x - 2) = 2x (3x + 2) -1 (3x + 2) So 6x2 + x - 2= ( 3x + 2 ) ( 2x -1 ) check F O I L 6x2 -3x +4x -2 = 6x2 + x - 2