// Numbas version: exam_results_page_options {"name": "Factorise the quadratic expression - Refresh", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "preventleave": false, "showfrontpage": false}, "question_groups": [{"questions": [{"preamble": {"css": "", "js": ""}, "ungrouped_variables": ["a", "b", "c", "d"], "rulesets": {}, "extensions": [], "metadata": {"description": "

Testing factorisation of quadratics.

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The first step is to find two numbers that add together to give $\\var{a*d+c*b}$ and multiply to give $\\var{a*c} \\times \\var{b*d} = \\var{a*b*c*d}$.

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These are $\\var{a*d}$ and $\\var{c*b}$.

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We split the $x$-term using $\\simplify{{a + b}x = {a} x + {b} x}$ and work as follows:

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\\\begin{aligned}\\simplify{{a*c}x^2 + {a*d + c*b} x + {b*d}} &= \\simplify{{a*c}x^2 + {a*d} x + {c*b} x + {c*d}} \\\\ &= \\simplify{{a} x({c} x + {d}) + {b}({c}x + {d})} \\\\ &= \\simplify{({a}x + {b})({c}x + {d})}\\end{aligned}\

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constant in first factor

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x-coefficient in second factor

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constant in second factor

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x-coefficient in first factor

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Factorise the following quadratic.

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$\\simplify{{a*c}x^2 + {a*d + c*b}x + {b*d}}$

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