The value of $\\large\\simplify{({a}x^3+{b}x*y^2+{c}z^3)/((x+{d}y)(y+{f}z))}$ when $x = \\var{x}$, $y= \\var{y}$ and $z = \\var{z}$ is
", "variablesTest": {"maxRuns": 100, "condition": "x+d*y<>0 &\ny-f*z<>0 &\nz-f*y<>0 &\ny+f*z<>0 &\nx^3+b*x*y^2+c*z^3<>0"}, "preamble": {"css": "", "js": ""}, "parts": [{"choices": ["$\\simplify{{shuffledchoices[0]}}$
", "$\\simplify{{shuffledchoices[1]}}$
", "$\\simplify{{shuffledchoices[2]}}$
", "$\\simplify{{shuffledchoices[3]}}$
", "None of these
"], "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "shuffleChoices": false, "showFeedbackIcon": true, "maxMarks": 0, "scripts": {}, "matrix": "marks", "variableReplacementStrategy": "originalfirst", "marks": 0, "displayType": "radiogroup", "displayColumns": 0, "variableReplacements": []}], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "", "variable_groups": [], "ungrouped_variables": ["a", "b", "c", "d", "f", "x", "y", "z", "correctAnswer", "Choice1", "Choice2", "Choice3", "choices", "noneofthesemarks", "choicemarks", "marks", "shuffledchoices", "order"], "rulesets": {}, "name": "Q11", "variables": {"choices": {"name": "choices", "definition": "//choices, apart from \"none of the above\"\n [correctAnswer,Choice1,Choice2,Choice3]", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "noneofthesemarks": {"name": "noneofthesemarks", "definition": "//marks to award for selecting \"none of these\"\n 0", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "Choice1": {"name": "Choice1", "definition": "expression('(' + (a*x^3+b*x*y^2+c*z^3) + ')/((' + (x-d*y) +')(' + (y+f*z) + '))')", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "c": {"name": "c", "definition": "random(-2..2 except 0)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "a": {"name": "a", "definition": "random(1..4)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "choicemarks": {"name": "choicemarks", "definition": "//marks to award for each of the above choices\n [1,0,0,0]", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "y": {"name": "y", "definition": "random(-3..-1 except x except x/2)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "z": {"name": "z", "definition": "random(1..3 except -y)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "shuffledchoices": {"name": "shuffledchoices", "definition": "//the choice texts, in the shuffled order\n map(choices[j],j,order)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "correctAnswer": {"name": "correctAnswer", "definition": "expression('(' + (a*x^3+b*x*y^2+c*z^3) + ')/((' + (x+d*y) +')(' + (y+f*z) + '))')", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "x": {"name": "x", "definition": "random(-3..-1)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "order": {"name": "order", "definition": "//the order in which to display the choices - pick a random permutation of [0,1,2,3,4]\n deal(4)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "Choice3": {"name": "Choice3", "definition": "expression('(' + (a*x^3+b*x*y^2-c*z^3) + ')/((' + (x+d*y) +')(' + (y+f*z) + '))')", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "marks": {"name": "marks", "definition": "//marks to award for each choice, then append the marks for \"none of the above\"\n map(choicemarks[j],j,order)+noneofthesemarks", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "d": {"name": "d", "definition": "random(-3..3 except 0)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "f": {"name": "f", "definition": "random(-2..2 except 0)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "b": {"name": "b", "definition": "random(2..3)", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "Choice2": {"name": "Choice2", "definition": "expression('(' + (a*x^3-b*x*y^2+c*z^3) + ')/((' + (x+d*y) +')(' + (y+f*z) + '))')", "group": "Ungrouped variables", "templateType": "anything", "description": ""}}, "tags": [], "type": "question", "contributors": [{"name": "David Wishart", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1461/"}]}]}], "contributors": [{"name": "David Wishart", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1461/"}]}