Factorising polynomials using the highest common factor
", "notes": ""}, "type": "question", "preamble": {"js": "", "css": ""}, "statement": "Factorise the following expressions by taking out the highest common factor.
\nMake sure you input an asterisk (*) for multiplication wherever necessary.
\nFor example, $xy$ should be written as $x*y$, and $a(b+c)$ should be written as $a*(b+c)$.
", "question_groups": [{"pickQuestions": 0, "questions": [], "name": "", "pickingStrategy": "all-ordered"}], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "tags": [], "advice": "", "rulesets": {}, "name": "Marlon's copy of Factorisation", "parts": [{"vsetrangepoints": 5, "answersimplification": "all", "checkvariablenames": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "musthave": {"partialCredit": 0, "message": "Your answer must be factorised
", "strings": ["(", ")"], "showStrings": false}, "showpreview": true, "checkingaccuracy": 0.001, "variableReplacements": [], "scripts": {}, "prompt": "$\\var{c[0]}-\\var{c[1]}x^2=$
", "type": "jme", "answer": "2({c[0]}/2-{c[1]}/2x^2)", "marks": 1, "vsetrange": [0, 1], "expectedvariablenames": ["x", "a", "b", "c", "p", "q", "l", "m", "y"], "checkingtype": "absdiff"}, {"vsetrangepoints": 5, "answersimplification": "all", "checkvariablenames": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "musthave": {"partialCredit": 0, "message": "Your answer must be factorised
", "strings": ["(", ")"], "showStrings": false}, "showpreview": true, "checkingaccuracy": 0.001, "variableReplacements": [], "scripts": {}, "prompt": "$\\var{c[2]}ab+\\var{c[3]}bc=$
", "type": "jme", "answer": "2b*({c[2]}a/2+{c[3]}c/2)", "marks": 1, "vsetrange": [0, 1], "expectedvariablenames": ["x", "a", "b", "c", "p", "q", "l", "m", "y"], "checkingtype": "absdiff"}, {"vsetrangepoints": 5, "answersimplification": "all", "checkvariablenames": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "musthave": {"partialCredit": 0, "message": "Your answer must be factorised
", "strings": ["(", ")"], "showStrings": false}, "showpreview": true, "checkingaccuracy": 0.001, "variableReplacements": [], "scripts": {}, "prompt": "$\\var{c[4]}a^2+\\var{c[5]}ab=$
", "type": "jme", "answer": "2a*({c[4]}a/2+{c[5]}b/2)", "marks": 1, "vsetrange": [0, 1], "expectedvariablenames": ["x", "a", "b", "c", "p", "q", "l", "m", "y"], "checkingtype": "absdiff"}, {"vsetrangepoints": 5, "answersimplification": "all", "checkvariablenames": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "musthave": {"partialCredit": 0, "message": "Your answer must be factorised
", "strings": ["(", ")"], "showStrings": false}, "showpreview": true, "checkingaccuracy": 0.001, "variableReplacements": [], "scripts": {}, "prompt": "$pq^3-p^3q=$
", "type": "jme", "answer": "p*q*(q^2-p^2)", "marks": 1, "vsetrange": [0, 1], "expectedvariablenames": ["x", "a", "b", "c", "p", "q", "l", "m", "y"], "checkingtype": "absdiff"}, {"vsetrangepoints": 5, "answersimplification": "all", "checkvariablenames": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "musthave": {"partialCredit": 0, "message": "Your answer must be factorised
", "strings": ["(", ")"], "showStrings": false}, "showpreview": true, "checkingaccuracy": 0.001, "variableReplacements": [], "scripts": {}, "prompt": "$\\var{c2[0]}x^2y+\\var{c2[1]}xy^4=$
", "type": "jme", "answer": "3*x*y*({c2[0]}x/3+{c2[1]}y^3/3)", "marks": 1, "vsetrange": [0, 1], "expectedvariablenames": ["x", "a", "b", "c", "p", "q", "l", "m", "y"], "checkingtype": "absdiff"}, {"vsetrangepoints": 5, "answersimplification": "all", "checkvariablenames": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "musthave": {"partialCredit": 0, "message": "Your answer must be factorised
", "strings": ["(", ")"], "showStrings": false}, "showpreview": true, "checkingaccuracy": 0.001, "variableReplacements": [], "scripts": {}, "prompt": "$\\var{c3[0]}p^3q-\\var{c3[1]}p^2q^2+\\var{c3[2]}pq^3=$
", "type": "jme", "answer": "2*p*q*({c3[0]}p^2/2-{c3[1]}*p*q/2+{c3[2]}q^2/2)", "marks": 1, "vsetrange": [0, 1], "expectedvariablenames": ["x", "a", "b", "c", "p", "q", "l", "m", "y"], "checkingtype": "absdiff"}, {"vsetrangepoints": 5, "answersimplification": "all", "checkvariablenames": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "musthave": {"partialCredit": 0, "message": "Your answer must be factorised
", "strings": ["(", ")"], "showStrings": false}, "showpreview": true, "checkingaccuracy": 0.001, "variableReplacements": [], "scripts": {}, "prompt": "$\\var{c2[2]}lm^2-\\var{c2[3]}l^3m^3+\\var{c2[4]}l^2m^4=$
", "type": "jme", "answer": "3*l*m^2*({c2[2]}/3-{c2[3]}*l^2*m/3+{c2[4]}l*m^2/3)", "marks": 1, "vsetrange": [0, 1], "expectedvariablenames": ["x", "a", "b", "c", "p", "q", "l", "m", "y"], "checkingtype": "absdiff"}], "variables": {"c": {"definition": "shuffle([2,2,6,8,10,14])", "templateType": "anything", "name": "c", "description": "Coefficients in a,b,c (HCF: 2)
", "group": "Ungrouped variables"}, "c2": {"definition": "shuffle([3,3,6,9,15])[0..5]", "templateType": "anything", "name": "c2", "description": "Coefficients in e,f (HCF: 3)
", "group": "Ungrouped variables"}, "c3": {"definition": "shuffle([2,4,6,10,14])[0..3]", "templateType": "anything", "name": "c3", "description": "Part f (HCF:2)
", "group": "Ungrouped variables"}}, "ungrouped_variables": ["c", "c2", "c3"], "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}]}], "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}