// Numbas version: finer_feedback_settings {"name": "Factorising: Common factor", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Factorising: Common factor", "tags": ["algebra", "common factor", "distributive law", "factor", "factorisation", "Factorisation", "factorising"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"pxcoeff": {"name": "pxcoeff", "group": "part a", "definition": "primes[1]", "description": "", "templateType": "anything", "can_override": false}, "cmult": {"name": "cmult", "group": "part c", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "ct1": {"name": "ct1", "group": "part c", "definition": "cx*cmult", "description": "", "templateType": "anything", "can_override": false}, "ct2": {"name": "ct2", "group": "part c", "definition": "cmult*cy", "description": "", "templateType": "anything", "can_override": false}, "nconstant": {"name": "nconstant", "group": "part b", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "cc": {"name": "cc", "group": "part c", "definition": "-cprimes[2]", "description": "", "templateType": "anything", "can_override": false}, "nxcoeff": {"name": "nxcoeff", "group": "part b", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "ct3": {"name": "ct3", "group": "part c", "definition": "cmult*cc", "description": "", "templateType": "anything", "can_override": false}, "cf": {"name": "cf", "group": "part b", "definition": "-gcd(bp1,bp2)", "description": "", "templateType": "anything", "can_override": false}, "bc": {"name": "bc", "group": "part b", "definition": "bp2/cf", "description": "", "templateType": "anything", "can_override": false}, "pmult": {"name": "pmult", "group": "part a", "definition": "primes[0]", "description": "", "templateType": "anything", "can_override": false}, "bp1": {"name": "bp1", "group": "part b", "definition": "nmult*nxcoeff", "description": "", "templateType": "anything", "can_override": false}, "cy": {"name": "cy", "group": "part c", "definition": "cprimes[1]", "description": "", "templateType": "anything", "can_override": false}, "bp2": {"name": "bp2", "group": "part b", "definition": "nmult*nconstant", "description": "", "templateType": "anything", "can_override": false}, "pconstant": {"name": "pconstant", "group": "part a", "definition": "primes[2]", "description": "", "templateType": "anything", "can_override": false}, "cprimes": {"name": "cprimes", "group": "part c", "definition": "shuffle([2,3,5,7,11])[0..3]", "description": "", "templateType": "anything", "can_override": false}, "cx": {"name": "cx", "group": "part c", "definition": "cprimes[0]", "description": "", "templateType": "anything", "can_override": false}, "bx": {"name": "bx", "group": "part b", "definition": "bp1/cf", "description": "", "templateType": "anything", "can_override": false}, "primes": {"name": "primes", "group": "part a", "definition": "shuffle([2,3,5,7,11])[0..3]", "description": "", "templateType": "anything", "can_override": false}, "nmult": {"name": "nmult", "group": "part b", "definition": "random(-12..-2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "part a", "variables": ["pmult", "pxcoeff", "pconstant", "primes"]}, {"name": "part b", "variables": ["nmult", "nxcoeff", "nconstant", "bp2", "bp1", "cf", "bx", "bc"]}, {"name": "part c", "variables": ["cprimes", "cx", "cy", "cc", "cmult", "ct1", "ct2", "ct3"]}], "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": "

The expression $\\var{pmult*pxcoeff}x+\\var{pconstant*pmult}$ is a sum and can be factorised (written as a product) by finding the largest common factor:

$\\var{pmult*pxcoeff}x+\\var{pconstant*pmult} = $ [[0]] $\\large($ [[1]] $\\large)$

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We put the common factor out the front of a set of brackets and put the 'left-overs' inside.

The (largest) common factor of $\\var{pmult*pxcoeff}x+\\var{pconstant*pmult}$ is $\\var{pmult}$.

Once we remove that factor from each term in $\\var{pmult*pxcoeff}x+\\var{pconstant*pmult}$ we are left with $\\var{pxcoeff}x+\\var{pconstant}$.

That means $\\var{pmult*pxcoeff}x+\\var{pconstant*pmult}= \\var{pmult}(\\var{pxcoeff}x+\\var{pconstant})$.

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Factorise $\\simplify{{bp1}a+{bp2}}$

[[0]] $\\large($ [[1]] $\\large)$

Note: Choose the best common factor to minimise the total number of negative signs.

We put the common factor out the front of a set of brackets and put the 'left-overs' inside.

The common factor of $\\simplify{{bp1}a+{bp2}}$ that we should pull out is $\\var{cf}$. This is because:

$\\var{-cf}$ is the largest common factor and
by pulling the negative out the front as well, we avoid having two negative terms in the bracket.

Once we remove that factor from each term in $\\simplify{{bp1}a+{bp2}}$ we are left with $\\var{bx}a+\\var{bc}$.

That means $\\simplify{{bp1}a+{bp2}}$ is $\\var{cf} = \\var{cf}(\\var{bx}a+\\var{bc})$.

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Factorise $\\simplify{{ct1}x+{ct2}y+{ct3}}$

[[0]] $\\large($ [[1]] $\\large)$

We put the common factor out the front of a set of brackets and put the 'left-overs' inside.

The (largest) common factor of $\\simplify{{ct1}x+{ct2}y+{ct3}}$ is $\\var{cmult}$.

Once we remove that factor from each term in $\\simplify{{ct1}x+{ct2}y+{ct3}}$ we are left with $\\simplify{{cx}x+{cy}y+{cc}}$.

That means $\\simplify{{ct1}x+{ct2}y+{ct3}} = \\simplify{{cmult}({ct1}x+{ct2}y+{ct3})}$.

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