// Numbas version: finer_feedback_settings
{"name": "Factorise the quadratic expression (with non-trivial x^2)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"css": "", "js": ""}, "statement": "<p>Factorise the following quadratic.</p>", "tags": [], "variables": {"c": {"group": "Ungrouped variables", "definition": "random(-5..5#1)", "templateType": "randrange", "name": "c", "description": "<p>x-coefficient in second factor</p>"}, "d": {"group": "Ungrouped variables", "definition": "random(-5..5#1)", "templateType": "randrange", "name": "d", "description": "<p>constant in second factor</p>"}, "b": {"group": "Ungrouped variables", "definition": "random(-5..5#1)", "templateType": "randrange", "name": "b", "description": "<p>constant in first factor</p>"}, "a": {"group": "Ungrouped variables", "definition": "random(-5..5#1)", "templateType": "randrange", "name": "a", "description": "<p>x-coefficient in first factor</p>"}}, "ungrouped_variables": ["a", "b", "c", "d"], "variablesTest": {"maxRuns": 100, "condition": "(b/a <> d/c)\nand \n(a <> 0)\nand\n(b <> 0)\nand\n(c <> 0)\nand\n(d <> 0)\nand\n(gcd(a,b) = 1)\nand\n(gcd(c,d) = 1)"}, "rulesets": {}, "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Testing factorisation of quadratics.</p>"}, "name": "Factorise the quadratic expression (with non-trivial x^2)", "extensions": [], "parts": [{"variableReplacements": [], "checkingtype": "absdiff", "showpreview": true, "showFeedbackIcon": true, "marks": "2", "vsetrange": [0, 1], "expectedvariablenames": [], "type": "jme", "prompt": "<p>$\\simplify{{a*c}x^2 + {a*d + c*b}x + {b*d}}$</p>", "variableReplacementStrategy": "originalfirst", "answer": "({a}x+{b})({c}x+{d})", "vsetrangepoints": 5, "musthave": {"strings": ["(", ")"], "partialCredit": 0, "message": "", "showStrings": false}, "checkingaccuracy": 0.001, "scripts": {}, "showCorrectAnswer": true, "checkvariablenames": false, "notallowed": {"strings": ["^"], "partialCredit": 0, "message": "", "showStrings": false}}], "variable_groups": [], "advice": "<p>The first step is to find two numbers that add together to give $\\var{a*d+c*b}$ and multiply to give $\\var{a*c} \\times \\var{b*d} = \\var{a*b*c*d}$.</p>\n<p></p>\n<p>These are $\\var{a*d}$ and $\\var{c*b}$.</p>\n<p></p>\n<p>We split the $x$-term using $\\simplify{{a + b}x = {a} x + {b} x}$ and work as follows:</p>\n<p>\\[\\begin{aligned}\\simplify{{a*c}x^2 + {a*d + c*b} x + {b*d}} &amp;= \\simplify{{a*c}x^2 + {a*d} x + {c*b} x + {c*d}} \\\\ &amp;= \\simplify{{a} x({c} x + {d}) + {b}({c}x + {d})} \\\\ &amp;= \\simplify{({a}x + {b})({c}x + {d})}\\end{aligned}\\]</p>", "type": "question", "contributors": [{"name": "Andrew Stacey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1605/"}], "resources": []}]}], "contributors": [{"name": "Andrew Stacey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1605/"}]}