Factorise 12x^2 +17x +6
If you imaging the equation as ax^2 +bx +cYou multiply the numbers of a and c together. This number then becomes the product of two numbers that either add or subtract to make the number for b.So 12 x 6 is 72. You can then divide 72 in these combinations: 2 and 36, 4 and 18, 6 and 12, 8 and 9.Only one combination can make 17... 8 and 9.You then expand the quadratic equation, replacing 17x with 8x +9x ...(12x^2 +8x +9x +6)Half the equation and factorise just 12x^2 +8x..... so it becomes 4x(3x +2)Do the same with the other half +9x +6 becomes 3(3x +2)You'll notice the brackets are the same. You just combine the numbers outside of the brackets into one bracket and keep the other bracket to form: (4x +3)(3x +2).Sorted.
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