// Numbas version: finer_feedback_settings
{"name": "Luis's copy of Divide Polynomials", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "showQuestionGroupNames": false, "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": ["algebra", "algebraic manipulation", "checked2015", "dividing polynomials", "division of polynomials", "polynomial division", "quotient polynomial", "remainder polynomial"], "metadata": {"description": "<p>Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"variableReplacements": [], "gaps": [{"notallowed": {"strings": ["."], "message": "<p>Input numbers as integers not decimals.</p>", "showStrings": false, "partialCredit": 0}, "expectedvariablenames": [], "vsetrangepoints": 5, "checkingaccuracy": 0.001, "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "answersimplification": "std", "checkingtype": "absdiff", "showpreview": true, "marks": 1, "type": "jme", "vsetrange": [0, 1], "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}, "answer": "(({m} * (x ^ 2)) + ({n} * x) + {t})"}, {"variableReplacements": [], "minValue": "{t*n+be-t*s}", "maxValue": "{t*n+be-t*s}", "allowFractions": false, "marks": 2, "type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false}], "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "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      ", "variableReplacementStrategy": "originalfirst"}], "variables": {"be": {"name": "be", "definition": "random(-9..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "s1": {"name": "s1", "definition": "random(1,-1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "n": {"name": "n", "definition": "random(-9..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "s2": {"name": "s2", "definition": "random(1,-1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "s": {"name": "s", "definition": "s1*random(1..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "t": {"name": "t", "definition": "s2*random(-9..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "al": {"name": "al", "definition": "random(-9..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "r": {"name": "r", "definition": "1", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "m": {"name": "m", "definition": "1", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "name": "Luis's copy of Divide Polynomials", "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>", "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["be", "s2", "s1", "m", "al", "n", "s", "r", "t"], "type": "question", "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0}], "functions": {}, "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "variable_groups": [], "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  ", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}