// Numbas version: exam_results_page_options
{"name": "Dividing polynomials 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Dividing polynomials 2", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "cancelling common terms in algebraic fractions", "factorising polynomials", "polynomials", "rational polynomials", "simplifying algebraic fractions"], "advice": "<p>Note that both the numerator and denominator factorize and that they then have a common factor which can then be cancelled.</p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "\n      \n      \n      <p>$A=\\;\\;$[[0]]</p>\n      \n      \n      \n      <p>Input all numbers as integers or fractions and not as decimals.</p>\n      \n      \n      ", "gaps": [{"notallowed": {"message": "<p>Reduce to its lowest form.</p>", "showstrings": false, "strings": ["^4", "^(4)"], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 1.0, "answer": "((({m} * (x ^ 2)) + {(( - p) * q)}) / ((x ^ 2) + {n}))", "type": "jme"}], "type": "gapfill", "marks": 0.0}], "extensions": [], "statement": "\n  <p>Simplify the following expression:</p>\n  <p>\\[A=\\simplify[std]{({m} * x ^ 4 + {m -(p * q)} * x ^ 2 + {( -p) * q}) / (x ^ 4 + {1 + n} * x ^ 2 + {n})}\\]</p>\n  <p>Your answer should be as a single algebraic fraction in its lowest form.</p>\n  ", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"sq": {"definition": "random(1,-1)", "name": "sq"}, "sp": {"definition": "random(1,-1)", "name": "sp"}, "m": {"definition": "sm*random(1..5)", "name": "m"}, "n": {"definition": "sn*random(1..5)", "name": "n"}, "q": {"definition": "sq*random(1..5)", "name": "q"}, "p": {"definition": "sp*random(1..5)", "name": "p"}, "sn": {"definition": "random(1,-1)", "name": "sn"}, "sm": {"definition": "random(1,-1)", "name": "sm"}}, "metadata": {"notes": "\n                    \t\t<p><strong>27/06/2012:</strong></p>\n                    \t\t<p>Minor changes in display and statements/prompts.</p>\n                    \t\t<p>Added tags.</p>\n                    \t\t<p>Could have more detailed advice.</p>\n                    \t\t<p><strong>18/07/2012:</strong></p>\n                    \t\t<p>Added description.</p>\n                    \t\t<p><strong>23/07/2012:</strong></p>\n                    \t\t<p>Added tags.</p>\n                    \t\t<p>The Advice section is very brief - Should there be more help provided here?</p>\n                    \t\t<p>Question appears to be working correctly.</p>\n                    \t\t", "description": "<p>Algebraic manipulation/simplification.</p>\n        <p>Simplify $\\displaystyle \\frac{ax^4+bx^2+c}{a_1x^4+b_1x^2+c_1}$ by cancelling a a common degree 2 factor.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}