// Numbas version: exam_results_page_options
{"name": "Dado que $({x+{d}})$ es un factor de $g(x) =\u00a0ax^3+{b}x^2+{x}+m$, Encontrar el valor de $m$.", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Dado que $({x+{d}})$ es un factor de $g(x) =\u00a0ax^3+{b}x^2+{x}+m$, Encontrar el valor de $m$.", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>El teorema del factor establece que si $ f (x) $ es un polinomio y $ f (p) = 0 $, entonces $ (x-p) $ es un factor de $ f (x) $.</p>", "advice": "<p>Usando el teorema del factor, sabemos que si&nbsp;$(x-a)$ es un factor de un polinomio $f(x)$, entonces $f(a)=0$.</p>\n<p>Se nos da que $(\\simplify{x+{d}})$ es a factor of $g(x) =&nbsp;\\simplify{{w}*x^3+({w}{d}+{a}+{w}{b})*x^2+({a}{d}+{w}{b}{d}+{a}{b})*x+m}$.</p>\n<p>Por el teorema del factor, esto significa que $g(\\simplify{-{d}}) = 0$.</p>\n<div class=\"tlid-input input\">\n<div class=\"source-wrap\">\n<div class=\"input-full-height-wrapper tlid-input-full-height-wrapper\">\n<div class=\"source-input\">\n<div class=\"source-header\">\n<div class=\"go-wrap\"></div>\n</div>\n</div>\n</div>\n</div>\n</div>\n<div class=\"tlid-results-container results-container\">\n<div class=\"tlid-result result-dict-wrapper\">\n<div class=\"result tlid-copy-target\">\n<div class=\"text-wrap tlid-copy-target\">\n<div class=\"result-shield-container tlid-copy-target\"><span class=\"tlid-translation translation\"><span title=\"\" class=\"\">Sustituyendo&nbsp;&nbsp;</span></span>$x=\\simplify{-{d}}$ sobre $g(x)$ obtenemos</div>\n</div>\n</div>\n</div>\n</div>\n<p>\\[<br/>\\begin{align}<br/>g(\\simplify{-{d}}) &amp;= \\simplify[all,!collectNumbers]{{coef_x3}+{coef_x2}+{coef_x}+m}\\\\<br/>&amp;=\\simplify{{coef_x3}+{coef_x2}+{coef_x}+m}.<br/>\\end{align}<br/>\\]</p>\n<p>Por lo tanto, como $g(\\simplify{-{d}}) = 0$, tenemos</p>\n<p>\\[<br/>\\begin{align}<br/>\\simplify{{coef_x3}+{coef_x2}+{coef_x}+m}&amp;=0\\\\<br/>m&amp;=\\simplify{-({coef_x3}+{coef_x2}+{coef_x})}.<br/>\\end{align}<br/>\\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"coef_x": {"name": "coef_x", "group": "Ungrouped variables", "definition": "(a*d+w*b*d+a*b)*(-d)", "description": "<p>Number obtained by putting x=-d into the third term of the equation.</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-2..3 except 0)", "description": "<p>Random number between -2 and 3, not including 0 for creating polynomial.</p>", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-2..2 except 0 except a except b)", "description": "<p>Used in creation of the polynomial.</p>", "templateType": "anything", "can_override": false}, "w": {"name": "w", "group": "Ungrouped variables", "definition": "random(2,3,4)", "description": "<p>Random number between 2,3,4.</p>", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-2..3 except 0)", "description": "<p>Random number between -2 and 3 except 0 for creating polynomial.</p>", "templateType": "anything", "can_override": false}, "coef_x3": {"name": "coef_x3", "group": "Ungrouped variables", "definition": "(w)*(-d)^3", "description": "<p>Number obtained by putting x=-d into the first term of the equation.</p>", "templateType": "anything", "can_override": false}, "coef_x2": {"name": "coef_x2", "group": "Ungrouped variables", "definition": "(w*d+a+w*b)*(-d)^2", "description": "<p>Number obtained by putting x=-d into the second term of the equation.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["w", "a", "b", "d", "coef_x3", "coef_x2", "coef_x"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Dado que $(\\simplify{x+{d}})$ es un factor de $g(x) =&nbsp;\\simplify{{w}*x^3+({w}{d}+{a}+{w}{b})*x^2+({a}{d}+{w}{b}{d}+{a}{b})*x}+m$, Encontrar el valor de $m$.</p>\n<p>$m =$ [[0]].</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{-({w}*({-d})^3+({w}*{d}+{a}+{w}*{b})*({-d})^2+({a}*{d}+{w}*{b}*{d}+{a}*{b})*{-d})}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}