// Numbas version: finer_feedback_settings
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"templateType": "anything", "can_override": false}, "factor2": {"name": "factor2", "group": "b", "definition": "random('\\$x\\$','\\$x^2\\$','\\$xy\\$','\\$x^2y\\$','\\$xy^2\\$','\\$x^2y^2\\$','\\$(x+1)\\$','\\$(y-1)^3\\$')", "description": "", "templateType": "anything", "can_override": false}, "failsafepowerp1": {"name": "failsafepowerp1", "group": "Ungrouped variables", "definition": "failsafepower+1", "description": "", "templateType": "anything", "can_override": false}, "xconstantpower": {"name": "xconstantpower", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything", "can_override": false}, "primepower": {"name": "primepower", "group": "Ungrouped variables", "definition": "random(1,2)", "description": "", "templateType": "anything", "can_override": false}, "xcpowerp1": {"name": "xcpowerp1", "group": "Ungrouped variables", "definition": "xconstantpower+1", "description": "", "templateType": "anything", "can_override": false}, 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"anything", "can_override": false}, "ypower": {"name": "ypower", "group": "Ungrouped variables", "definition": "random(0..3)", "description": "", "templateType": "anything", "can_override": false}, "failsafepowerm1": {"name": "failsafepowerm1", "group": "Ungrouped variables", "definition": "failsafepower-1", "description": "", "templateType": "anything", "can_override": false}, "xcpowerm1": {"name": "xcpowerm1", "group": "Ungrouped variables", "definition": "xconstantpower-1", "description": "", "templateType": "anything", "can_override": false}, "p2pp": {"name": "p2pp", "group": "Ungrouped variables", "definition": "prime^primepower", "description": "", "templateType": "anything", "can_override": false}, "gmarks": {"name": "gmarks", "group": "Ungrouped variables", "definition": "[1,\n  if(primepower>=1,1,0),\n  if(primepower>=2,1,0),1]+if(xpower<2 and ypower<2 and xconstantpower<2,[1,0],if(xconstantpower>1,[1,0],[0])+if(xpower>=1 and ypower>=1 and (xpower>2 or ypower>2),[1,if(xpower>=2 and ypower>=2,1,0),if(xpower>=2,1,0)],[if(xpower>=1,1,0),if(ypower>=1,1,0)])+if(primepower>=1 and xconstantpower>=1, [1],[]))", "description": "", "templateType": "anything", "can_override": false}, "xconstant": {"name": "xconstant", "group": "Ungrouped variables", "definition": "random(1..12)", "description": "", "templateType": "anything", "can_override": false}, "failsafepower": {"name": "failsafepower", "group": "Ungrouped variables", "definition": "if(xpower<2 and ypower<2 and xconstantpower<2,3,0 )", "description": "", "templateType": "anything", "can_override": false}, "failconstant": {"name": "failconstant", "group": "Ungrouped variables", "definition": "random(1..12 except xconstant)", "description": "", "templateType": "anything", "can_override": false}, "xpower": {"name": "xpower", "group": "Ungrouped variables", "definition": "random(0..3)", "description": "", "templateType": "anything", "can_override": false}, "expanded": {"name": "expanded", "group": "Ungrouped variables", "definition": "expression(\n  '1'+'*'+\n join(\n  repeat(prime,primepower)\n    +repeat(expression('x'),xpower)\n    +repeat(expression('y'),ypower)\n    ,    '*')\n  +if(xconstantpower>0,\n    '*('+join(repeat(expression('(x+{xconstant})'),xconstantpower), ')*(')+')','')\n  +if(failsafepower>0,\n    '*('+join(repeat(expression('(z+{failconstant})'),failsafepower), ')*(')+')','')\n)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["prime", "primepower", "p2pp", "expanded", "xpower", "ypower", "xconstant", "xconstantpower", "failconstant", "failsafepower", "failsafepowerm1", "failsafepowerp1", "xcpowerm1", "xcpowerp1", "choices", "gmarks"], "variable_groups": [{"name": "b", "variables": ["factor1", "factor2"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which of the following are factors of $\\simplify{{prime^primepower}x^{xpower}y^{ypower}(x+{xconstant})^{xconstantpower} (z+{failconstant})^{failsafepower}}$?</p>", "stepsPenalty": "10", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Factors are things that multiply to make a product.&nbsp;</p>\n<p>Consider the product $\\simplify{{prime^primepower}x^{xpower}y^{ypower}(x+{xconstant})^{xconstantpower} (z+{failconstant})^{failsafepower}}$.&nbsp;</p>\n<p>We can write this product as&nbsp;</p>\n<p>$\\simplify[basic, alwaystimes]{{expanded}}$</p>\n<p>Any combination of the above factors will still be a factor (since we can rearrange the product so that our collection of factors are all together and we can treat that collection as a single factor).<em></em></p>"}], "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": "choices", "matrix": "gmarks"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Suppose that $\\var{factor1}${factor2} is a factor of an expression. What can be said of $-\\var{factor1}${factor2}?</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Since $-1$ can divide every number (just like $1$ can), if a positive number is a factor, then so is the negative of it.</p>\n<p>In particular, if $\\var{factor1}${factor2} is a factor of an expression, then that expression can be written as a product involving $\\var{factor1}${factor2}, for instance $\\var{factor1}${factor2}$w$ where $w$ is the other factor. Notice then that we can write the expression as $-\\var{factor1}${factor2}$(-w)$, that is, $-\\var{factor1}${factor2} is also a factor.</p>"}], "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>It is also a factor.</p>", "<p>It&nbsp;is not&nbsp;necessarily a factor.</p>", "<p>It is definitely&nbsp;not a factor.</p>"], "matrix": ["1", 0, 0], "distractors": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "resources": []}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}