// Numbas version: exam_results_page_options
{"name": "The Factor Theorem", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "variable_groups": [], "tags": ["Factors", "factors", "polynomial long division", "polynomials", "remainders", "roots"], "name": "The Factor Theorem", "functions": {}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": ""}, "ungrouped_variables": ["c", "d"], "parts": [{"variableReplacementStrategy": "originalfirst", "distractors": ["", "", "", ""], "steps": [{"variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "information", "prompt": "<p>The Factor Theorem says that $x-a$ is a factor of a polynomial $f(x)$ if and only if $f(a)=0$.&nbsp;</p>\n<p>Since we are told that $f(\\var{c})=0$ then we know $\\simplify{x-{c}}$ is a factor of $f(x)$.</p>", "variableReplacements": [], "scripts": {}, "marks": 0}], "maxMarks": 0, "displayColumns": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "marks": 0, "displayType": "radiogroup", "stepsPenalty": 0, "type": "1_n_2", "choices": ["<p>$\\simplify{x-{c}}$ is a factor of $f(x)$</p>", "<p>$\\simplify{x+{c}}$ is a factor of $f(x)$</p>", "<p>$x$ is a factor of $f(x)$</p>", "<p>$\\var{c}$ is a factor of $f(x)$</p>"], "matrix": ["1", 0, 0, 0], "prompt": "<p>Suppose a polynomial $f(x)$ evaluated at $\\var{c}$&nbsp;is $0$, that is, $f(\\var{c})=0$.&nbsp;</p>\n<p>Which of the following is&nbsp;guaranteed?&nbsp;</p>", "minMarks": 0, "shuffleChoices": false}, {"variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "information", "prompt": "<p>The Factor Theorem says that $x-a$ is a factor of a polynomial $f(x)$ if and only if $f(a)=0$.&nbsp;&nbsp;</p>\n<p>Since we are told&nbsp;$\\simplify{x-{d}}$ is a factor of $g(x)$,&nbsp;we know&nbsp;that $g(\\var{d})=0$.</p>", "variableReplacements": [], "scripts": {}, "marks": 0}], "scripts": {}, "stepsPenalty": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "gapfill", "prompt": "<p>Suppose $\\simplify{x-{d}}$ is a factor of a polynomial $g(x)$. That is, if we divided $g(x)$ by $\\simplify{x-{d}}$ the remainder would be&nbsp;$0$.</p>\n<p>This&nbsp;guarantees&nbsp;us that $g\\large($ [[0]]&nbsp;$\\large)=$&nbsp;[[1]].</p>", "variableReplacements": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "showCorrectAnswer": true, "allowFractions": false, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "minValue": "{d}", "scripts": {}, "marks": 1, "showFeedbackIcon": true, "mustBeReduced": false, "type": "numberentry", "correctAnswerFraction": false, "maxValue": "{d}"}, {"variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "showCorrectAnswer": true, "allowFractions": false, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "minValue": "0", "scripts": {}, "marks": 1, "showFeedbackIcon": true, "mustBeReduced": false, "type": "numberentry", "correctAnswerFraction": false, "maxValue": "0"}], "marks": 0}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"c": {"description": "", "definition": "random(-12..12 except 0)", "templateType": "anything", "name": "c", "group": "Ungrouped variables"}, "d": {"description": "", "definition": "random(-12..12 except [0,c])", "templateType": "anything", "name": "d", "group": "Ungrouped variables"}}, "extensions": [], "type": "question", "preamble": {"js": "", "css": ""}, "advice": "", "statement": "", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}