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Mastering Quadratic Factorization: Simplifying Difficult Quadratics

Learn an alternative method to factorize challenging quadratic expressions like 12x^2 + 28x + 15 without trial and error. Follow step-by-step instructions for factorizing, including finding product pairs and combining factors correctly. Enhance your factorization skills and practice with example problems.

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Mastering Quadratic Factorization: Simplifying Difficult Quadratics

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

  2. How to factorise 12x2+28x+15 1 Multiply the 12 and 15 12x2 + 28x+ 15 18 x 10 = 180 2 Find factors of this product (180) whose sum is the coefficient of x (28). 3 1 3 10 x 18 is 180 and 10 add 18 = 28 So our numbers are 10 and 18 2

  3. How to factorise We found our numbers are 10 and 18 1 Replace +28x with + 10x + 18x 12x2+ 10x + 18x + 15 12x2+ 28x + 15 2 Divide the expression into 2 parts 1 12x2 + 10x+ 18x + 15 2

  4. How to factorise We need to factorise both parts 1 Factorise the red part +6x(2x+3) 1 2 Factorise the blue part 12x2 + 18x+ 10x + 15 +5(2x+3) 2

  5. How to factorise Check that the bits inside the brackets are the same! 1 One of the factors is what is in brackets 6x(2x+3) 5(2x+3) 1 2 Combine what’s left for the other factor 2 (6x + 5) 3 Check your answer 3 (6x + 5) (2x+3) = 12x2+28x+15

  6. How to factorise 6x2+x-12 1 Multiply the 6 and -12 6x2 + x– 12 -8 x 9 = -72 2 Find factors of this product (-72) whose sum is the coefficient of x (1). 3 1 3 9 x -8 is -72 and 9 add minus 8 =1 So our numbers are 9 and -8 2

  7. How to factorise We found our numbers are +9 and - 8 1 Replace +x with + 9x - 8x 6x2+ 9x – 8x - 12 6x2+ x – 12 2 Divide the expression into 2 parts 1 6x2 + 9x– 8x - 12 2

  8. How to factorise We need to factorise both parts 1 Factorise the red part 3x(2x+3) 1 2 Factorise the blue part 6x2 + 9x– 8x - 12 -4(2x+3) 2

  9. How to factorise Check that the bits inside the brackets are the same! 1 One of the factors is what is in brackets 3x(2x+3) -4(2x+3) 1 2 Combine what’s left for the other factor 2 (3x - 4) 3 Check your answer 3 (3x - 4) (2x+3) = 6x2+x-12

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

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