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{"name": "Algebra III: factorisation (finding factors)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["prime", "primepower", "p2pp", "xpower", "ypower", "xconstant", "xconstantpower", "failconstant", "failsafepower", "failsafepowerm1", "failsafepowerp1", "xcpowerm1", "xcpowerp1", "choices", "marks", "maxmarks", "m"], "name": "Algebra III: factorisation (finding factors)", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": 0, "maxAnswers": "0", "displayColumns": 0, "prompt": "<p>Which of the following are factors of $\\simplify{{prime^primepower}x^{xpower}y^{ypower}(x+{xconstant})^{xconstantpower} (z+{failconstant})^{failsafepower}}$?</p>", "matrix": "marks", "shuffleChoices": true, "maxMarks": "0", "variableReplacements": [], "minAnswers": "0", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>A factor can be a number ($3$), a variable ($x$), or a combination ($17x^2$). A factor could even be an expression with more than one term ($x+1$).</p>\n<p>If it is an exact divisor of the&nbsp;expression or term being factorised, without a remainder, then it is indeed a factor. For example, $\\frac{4x(x+1)}{2x}=2(x+1)$ Here, the term $2x$ divides and simplifies the original expression without a remainder term being added.</p>\n<p>For this question, try to divide the given expression by each of the options provided and select the factors as described above.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "warningType": "none", "marks": 0, "choices": "choices", "type": "m_n_2", "displayType": "checkbox", "minMarks": "0"}, {"stepsPenalty": 0, "displayColumns": 0, "prompt": "<p>Suppose that $\\var{factor1}${factor2} is a factor of an expression. What can be said of $-\\var{factor1}${factor2}?</p>", "matrix": ["1", 0, 0], "shuffleChoices": false, "maxMarks": 0, "variableReplacements": [], "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>"], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>A factor can also be negative. This is often useful when simplifying algebraic expressions. For instance, take the expression $-4x-8$. When the factor $-4$ is taken out, the resulting expression is $-4(x+2)$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "distractors": ["", "", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}], "extensions": [], "statement": "", "variable_groups": [{"variables": ["factor1", "factor2"], "name": "b"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"prime": {"definition": "random(2,3,5,7)", "templateType": "anything", "group": "Ungrouped variables", "name": "prime", "description": ""}, "factor1": {"definition": "random(2..144)", "templateType": "anything", "group": "b", "name": "factor1", "description": ""}, "factor2": {"definition": "random('\\$x\\$','\\$x^2\\$','\\$xy\\$','\\$x^2y\\$','\\$xy^2\\$','\\$x^2y^2\\$','\\$(x+1)\\$','\\$(y-1)^3\\$')", "templateType": "anything", "group": "b", "name": "factor2", "description": ""}, "failsafepowerp1": {"definition": "failsafepower+1", "templateType": "anything", "group": "Ungrouped variables", "name": "failsafepowerp1", "description": ""}, "xconstantpower": {"definition": "random(0..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "xconstantpower", "description": ""}, "primepower": {"definition": "random(1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "primepower", "description": ""}, "xpower": {"definition": "random(0..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "xpower", "description": ""}, "m": {"definition": "length(choices)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "xcpowerp1": {"definition": "xconstantpower+1", "templateType": "anything", "group": "Ungrouped variables", "name": "xcpowerp1", "description": ""}, "choices": {"definition": "['\\$1\\$','\\$\\\\var{prime}\\$','\\$\\\\var{prime^2}\\$','\\$\\\\simplify{{p2pp}x^{xpower}y^{ypower}(x+{xconstant})^{xconstantpower}(z+{failconstant})^{failsafepower}}  \\$']+if(xpower<2 and ypower<2 and xconstantpower<2,['\\$(z+'+failconstant+')^'+failsafepowerm1+'\\$','\\$(z+'+failconstant+')^'+failsafepowerp1+'\\$'],if(xconstantpower>1,['\\$\\\\simplify{(x+{xconstant})^{xcpowerm1}}\\$','\\$(x+'+xconstant+')^'+xcpowerp1+'\\$'],['\\$(x+'+xconstant+')^'+xcpowerp1+'\\$'])+if(xpower>=1 and ypower>=1 and (xpower>2 or ypower>2),['\\$xy\\$','\\$x^2y^2\\$','\\$x^2y\\$'],['\\$x\\$','\\$y\\$'])+if(primepower>=1 and xconstantpower>=1, ['\\$\\\\simplify{{prime} (x+{xconstant})^{xconstantpower}}\\$'],[]))", "templateType": "anything", "group": "Ungrouped variables", "name": "choices", "description": "<p>$\\simplify{{prime^primepower}x^{xpower}y^{ypower}(x+{xconstant})^{xconstantpower} (z+{failconstant})^{failsafepower}}$</p>"}, "ypower": {"definition": "random(0..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "ypower", "description": ""}, "failsafepowerm1": {"definition": "failsafepower-1", "templateType": "anything", "group": "Ungrouped variables", "name": "failsafepowerm1", "description": ""}, "maxmarks": {"definition": "length(choices)", "templateType": "anything", "group": "Ungrouped variables", "name": "maxmarks", "description": ""}, "xcpowerm1": {"definition": "xconstantpower-1", "templateType": "anything", "group": "Ungrouped variables", "name": "xcpowerm1", "description": ""}, "p2pp": {"definition": "prime^primepower", "templateType": "anything", "group": "Ungrouped variables", "name": "p2pp", "description": ""}, "marks": {"definition": "[1,if(primepower>=1,1,0),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],[]))", "templateType": "anything", "group": "Ungrouped variables", "name": "marks", "description": ""}, "failsafepower": {"definition": "if(xpower<2 and ypower<2 and xconstantpower<2,3,0 )", "templateType": "anything", "group": "Ungrouped variables", "name": "failsafepower", "description": ""}, "failconstant": {"definition": "random(1..12 except xconstant)", "templateType": "anything", "group": "Ungrouped variables", "name": "failconstant", "description": ""}, "xconstant": {"definition": "random(1..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "xconstant", "description": ""}}, "metadata": {"description": "<p>A brief look at all possible factors of a given algebraic expression.</p>\n<p><em>Adapted from&nbsp;</em><strong>'Factorisation: finding factors'</strong><em> by&nbsp;</em><strong>Ben Brawn</strong>.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Luke Park", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/826/"}]}]}], "contributors": [{"name": "Luke Park", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/826/"}]}