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$\\simplify{x^2 + {a + b}x + {a*b}}$
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", "checkingType": "absdiff", "customMarkingAlgorithm": ""}, {"extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "failureRate": 1, "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "jme", "answer": "(x+{d})(x+{b})", "vsetRange": [0, 1], "checkVariableNames": false, "showPreview": true, "checkingAccuracy": 0.001, "unitTests": [], "variableReplacements": [], "scripts": {}, "expectedVariableNames": [], "vsetRangePoints": 5, "prompt": "$\\simplify{x^2 + {d + b}x + {d*b}}$
", "checkingType": "absdiff", "customMarkingAlgorithm": ""}, {"extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "failureRate": 1, "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "jme", "answer": "(x+{a})(x+{f})", "vsetRange": [0, 1], "checkVariableNames": false, "showPreview": true, "checkingAccuracy": 0.001, "unitTests": [], "variableReplacements": [], "scripts": {}, "expectedVariableNames": [], "vsetRangePoints": 5, "prompt": "$\\simplify{x^2 + {a + f}x + {a*f}}$
", "checkingType": "absdiff", "customMarkingAlgorithm": ""}, {"extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "failureRate": 1, "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "jme", "answer": "(x+{g})(x+{f})", "vsetRange": [0, 1], "checkVariableNames": false, "showPreview": true, "checkingAccuracy": 0.001, "unitTests": [], "variableReplacements": [], "scripts": {}, "expectedVariableNames": [], "vsetRangePoints": 5, "prompt": "$\\simplify{x^2 + {f + g}x + {f*g}}$
", "checkingType": "absdiff", "customMarkingAlgorithm": ""}], "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": "a <> b\na <> 0\nb <> 0"}, "advice": "The first step is to find two numbers that add together to give $\\var{a+b}$ and multiply to give $\\var{a*b}$.
\n\nThese are $\\var{a}$ and $\\var{b}$.
\n\nWe split the $x$-term using $\\simplify{{a + b}x = {a} x + {b} x}$ and work as follows:
\n\\[\\begin{aligned}\\simplify{x^2 + {a + b} x + {a*b}} &= \\simplify{x^2 + {a} x + {b} x + {a*b}} \\\\ &= \\simplify{x(x + {a}) + {b}(x + {a})} \\\\ &= \\simplify{(x + {b})(x + {a})}\\end{aligned}\\]
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", "name": "a", "definition": "random(-9..9#1)", "templateType": "randrange"}, "g": {"group": "Ungrouped variables", "description": "", "name": "g", "definition": "random(-9..9 except 0)", "templateType": "anything"}, "b": {"group": "Ungrouped variables", "description": "The second factor.
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"}, "statement": "Factorise the following quadratic.
", "tags": [], "rulesets": {}, "type": "question", "contributors": [{"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}]}]}], "contributors": [{"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}]}