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

2. 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). 1 2 3 12x 2 + 28x + 15 1 2 3 10 x 18 is 180 and 10 add 18 = 28 So our numbers are 10 and 18 18 x 10 = 180

3. How to factorise Replace +28x with + 10x + 18x Divide the expression into 2 parts 1 2 12x 2 + 10x + 18x + 15 We found our numbers are 10 and 1 8 1 2 12x 2 + 10x + 18x + 15 12x 2 + 28x + 15

4. How to factorise Factorise the red part Factorise the blue part 1 2 We need to factorise both parts 1 2 12x 2 + 18x + 10x + 15 +6x(2x+3) +5(2x+3)

5. 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

6. 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). 1 2 3 6x 2 + x – 12 1 2 3 9 x -8 is -72 and 9 add minus 8 =1 So our numbers are 9 and -8 - 8 x 9 = - 72

7. 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 - 8 1 2 6x 2 + 9x – 8x - 12 6x 2 + x – 12

8. 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 - 12 3x(2x+3) -4(2x+3)

9. 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

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