An alternative to the trial and improvement method Factorising Difficult Quadratics.

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Quadratics ax2 + bx + c.

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Presentation transcript:

An alternative to the trial and improvement method Factorising Difficult Quadratics

How to factorise 12x 2 +28x+15 Multiply the 12 and 15 Find factors of this product (180) whose sum is the coefficient of x (28) x x x 18 is 180 and 10 add 18 = 28 So our numbers are 10 and x 10 = 180

How to factorise Replace +28x with + 10x + 18x Divide the expression into 2 parts x x + 18x + 15 We found our numbers are 10 and x x + 18x x x + 15

How to factorise Factorise the red part Factorise the blue part 1 2 We need to factorise both parts x x + 10x x(2x+3) +5(2x+3)

How to factorise One of the factors is what is in brackets Combine what’s left for the other factor 1 2 Check that the bits inside the brackets are the same! 1 2 (6x + 5) 6x(2x+3) 5(2x+3) 3 Check your answer (6x + 5) (2x+3) = 12x 2 +28x+15 3

How to factorise 6x 2 +x-12 Multiply the 6 and -12 Find factors of this product (-72) whose sum is the coefficient of x (1) x 2 + x – x -8 is -72 and 9 add minus 8 =1 So our numbers are 9 and x 9 = - 72

How to factorise Replace +x with + 9x - 8x Divide the expression into 2 parts 1 2 6x 2 + 9x – 8x - 12 We found our numbers are +9 and x 2 + 9x – 8x x 2 + x – 12

How to factorise Factorise the red part Factorise the blue part 1 2 We need to factorise both parts 1 2 6x 2 + 9x – 8x x(2x+3) -4(2x+3)

How to factorise One of the factors is what is in brackets Combine what’s left for the other factor 1 2 Check that the bits inside the brackets are the same! 1 2 (3x - 4) 3x(2x+3) -4(2x+3) 3 Check your answer (3x - 4) (2x+3) = 6x 2 +x-12 3

Note Remember not to delete your attempts. Even if you get the answer wrong, you may still get marks!