// Numbas version: exam_results_page_options
{"name": "The Remainder Theorem", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["n", "c", "rem"], "name": "The Remainder Theorem", "tags": ["Factors", "factors", "polynomial long division", "polynomials", "remainders", "roots"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Suppose a polynomial $f(x)$ of degree $\\var{n}$ is divided by $\\simplify{x-{c}}$ and the remainder is $\\var{rem}$.</p>\n<p>This guarantees&nbsp;us that $f\\large($ [[0]]&nbsp;$\\large)=$&nbsp;[[1]].</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The Remainder Theorem says that the remainder of dividing $f(x)$ by $x-a$ is equal to&nbsp;$f(a)$. So in this case we know $f(\\var{c})=\\var{rem}$.</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{c}", "minValue": "{c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{rem}", "minValue": "{rem}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"c": {"definition": "random(-12..12 except [0,n])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "n": {"definition": "random(3..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "rem": {"definition": "random(-12..12 except [c,n])", "templateType": "anything", "group": "Ungrouped variables", "name": "rem", "description": ""}}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}