,"difficultyBand":null,"totalMarks":2,"sourceTitle":"Factorising Harder Quadratics","calculatorUse":null,"parts":[{"id":"14a8841a-a335-4b3e-b116-765bc83b8d98","label":"a","content":"Factorise $2x^2 - 9x + 10$","markscheme":"- Identifies factors of $ac = 20$ that sum to -9 (-4 and -5) M1\n- Final answer $(x - 2)(2x - 5)$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Identifies factors of 20 that sum to -9.","code":"M"},{"id":"p2","marks":1,"description":"Final answer $(x - 2)(2x - 5)$.","code":"A"}],"finalAnswers":["(x - 2)(2x - 5)"],"generatedAt":"2026-05-07T02:06:38.085Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"ac_method","label":"Split the middle term","steps":[{"type":"text","order":0,"title":"Find the two factors","content":"Multiply the coefficient of $x^2$ by the constant: $2\\times10=20$. The factors $-4$ and $-5$ multiply to $20$ and add to $-9$, so identifying them earns **M1**.","highlights":[{"text":"Factorise $2x^2 - 9x + 10$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"2x^2-9x+10=\\htmlData{anchor=split}{\\color{@sky}{2x^2-4x-5x+10}}"},{"latex":"2x^2-4x-5x+10=\\htmlData{anchor=grouped}{\\color{@amber}{2x(x-2)-5(x-2)}}"},{"latex":"2x(x-2)-5(x-2)=\\htmlData{anchor=answer}{\\color{@green}{(x-2)(2x-5)}}"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"grouped","from":"split","color":"sky","label":"factor each pair","style":"solid"},{"to":"answer","from":"grouped","color":"green","label":"common bracket","style":"solid"}]},"order":1,"title":"Factor by grouping","description":"Split the middle term into -4x and -5x. Factorise each pair, then take out the common bracket; this final factorisation earns A1."}]},{"id":"trial_brackets","label":"Use two brackets","steps":[{"type":"text","order":0,"title":"Choose the factor pair","content":"First calculate $ac$: $2\\times10=20$. The factors $-4$ and $-5$ multiply to $20$ and add to $-9$, earning **M1**. Using positive $x$-terms, start the brackets with $2x$ and $x$.","highlights":[{"text":"Factorise $2x^2 - 9x + 10$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"2x^2-9x+10=2x^2-4x-5x+10"},{"latex":"2x^2-4x-5x+10=2x(x-2)-5(x-2)"},{"latex":"2x(x-2)-5(x-2)=\\htmlData{anchor=answer}{\\color{@green}{(x-2)(2x-5)}}"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"answer"}]},"order":1,"title":"Factor by grouping","description":"Split the middle term into -4x and -5x. Factor each pair, then take out the common bracket. The final factorisation earns A1."}]}],"generatedAt":"2026-07-21T03:09:40.437Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"6bf8e53a-f5aa-4e47-bc80-b75668c474a3","revisionId":"8842a515-0e30-4d22-9ddb-b74673c151c3","questionNumber":"9","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Factorising Harder Quadratics","calculatorUse":null,"parts":[{"id":"e7b592f3-e340-4ae7-87a2-4c8025ac2d86","label":"a","content":"Solve $5x^2 + 11x - 12 = 0$","markscheme":"- Factorises the quadratic into $(x + 3)(5x - 4)$ M1\n- Sets factors to zero to find solutions M1\n- Final answers $x = -3$ and $x = \\frac{4}{5}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correctly factorises the quadratic into $(x + 3)(5x - 4)$.","code":"M"},{"id":"p2","marks":1,"description":"Sets factors to zero to solve for $x$.","code":"M"},{"id":"p3","marks":1,"description":"Final answers $x = -3$ and $x = \\frac{4}{5}$.","code":"A"}],"finalAnswers":["x = -3, x = 4/5"],"generatedAt":"2026-05-07T02:06:38.085Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"factorising","label":"Factorise the quadratic","steps":[{"type":"text","order":0,"title":"Build

Factorising Harder Quadratics Questions

Factorising Harder Quadratics Questions

Factorising Harder Quadratics Questions

Factorising Harder Quadratics Questions