// Numbas version: exam_results_page_options {"name": "Polynomial division", "duration": 0, "metadata": {"description": "

Practice dividing polynomials using the long division method.

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Well done, you got every question right.

"}], "showactualmark": true, "showanswerstate": true, "intro": ""}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Polynomial division 2by1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "functions": {"s": {"definition": "latex(if(n=0,\"\",if(n<0,\"-\",\"+\")+abs(n)))", "type": "string", "language": "jme", "parameters": [["n", "number"]]}, "sx": {"definition": "latex(if(n=0,\"\",if(n<0,\"-\",\"+\")+if(abs(n)=1,\"\",abs(n))+\"x\"))", "type": "string", "language": "jme", "parameters": [["n", "number"]]}}, "ungrouped_variables": ["a", "b", "c", "d", "xcoeff", "con"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
[[0]][[1]]
$\\simplify{x+{a}}$$\\simplify{{b}*x^2}$${\\var{xcoeff}}$$\\var{con}$
[[2]][[3]]
[[4]][[5]]
[[6]][[7]]
[[8]]
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Write the final answer in the following form:

\n\n\n\n\n\n \n\n\n\n\n\n\n\n\n\n
$\\simplify{{b}*x^2+{c+a*b}*x+{a*c+d}}$$=$[[0]]$+$[[1]]
$\\simplify{x+{a}}$$\\simplify{x+{a}}$
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Divide the polynomial $\\simplify{{b}*x^2+{c+a*b}*x+{a*c+d}}$ by $\\simplify{x+{a}}$.

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Divide quadratic by linear

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[[0]][[1]][[2]]
$\\simplify{x+{a}}$$\\simplify{{b}*x^3}$${\\var{x2coeff}}$${\\var{xcoeff}}$$\\var{con}$
[[3]][[4]]
[[5]][[6]][[7]]
[[8]][[9]]
[[10]][[11]]
[[12]][[13]]
[[14]]
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[], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{r}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

Write the final answer in the following form:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\simplify{{b}*x^3+{c+a*b}*x^2+{a*c+d}*x+{a*d+r}}$$=$[[0]]$+$[[1]]
$\\simplify{x+{a}}$$\\simplify{x+{a}}$
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Divide the polynomial $\\simplify{{b}*x^3+{c+a*b}*x^2+{a*c+d}*x+{a*d+r}}$ by $\\simplify{x+{a}}$.

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "xcoeff": {"definition": "sx(a*c+d)", "templateType": "anything", "group": "Ungrouped variables", "name": "xcoeff", "description": ""}, "c": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "x2coeff": {"definition": "sx2(a*b+c)", "templateType": "anything", "group": "Ungrouped variables", "name": "x2coeff", "description": ""}, "r": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "con": {"definition": "s(a*d+r)", "templateType": "anything", "group": "Ungrouped variables", "name": "con", "description": ""}}, "metadata": {"description": "

Divide cubic by linear

", "licence": "None specified"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Polynomial division 3by2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "functions": {"s": {"definition": "latex(if(n=0,\"\",if(n<0,\"-\",\"+\")+if(abs(n)=1,\"\",abs(n))))", "type": "string", "language": "jme", "parameters": [["n", "number"]]}, "sx": {"definition": "latex(if(n=0,\"\",if(n<0,\"-\",\"+\")+if(abs(n)=1,\"\",abs(n))+\"x\"))", "type": "string", "language": "jme", "parameters": [["n", "number"]]}, "sx2": {"definition": "latex(if(n=0,\"\",if(n<0,\"-\",\"+\")+if(abs(n)=1,\"\",abs(n))+\"x^2\"))", "type": "string", "language": "jme", "parameters": [["n", "number"]]}}, "ungrouped_variables": ["x2coeff", "xcoeff", "con"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
[[0]][[1]]
$\\simplify{{a1}*x^2+{a2}*x+{a3}}$$\\simplify{{a1*b1}*x^3}$${\\var{x2coeff}}$${\\var{xcoeff}}$$\\var{con}$
[[2]][[3]][[4]]
[[5]][[6]][[7]]
[[8]][[9]][[10]]
[[11]][[12]]
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Write the final answer in the following form:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\simplify{{a1*b1}*x^3+{a1*b2+a2*b1}*x^2+{a2*b2+a3*b1+r1}*x+{a3*b2+r2}}$$=$[[0]]$+$[[1]]
$\\simplify{{a1}*x^2+{a2}*x+{a3}}$$\\simplify{{a1}*x^2+{a2}*x+{a3}}$
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Divide the polynomial $\\simplify{{a1*b1}*x^3+{a1*b2+a2*b1}*x^2+{a2*b2+a3*b1+r1}*x+{a3*b2+r2}}$ by $\\simplify{{a1}*x^2+{a2}*x+{a3}}$.

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Divide cubic by quadratic

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