Quiz — Serie d'exercices - Math - Polynomes - 2ème Sciences.pdf

Question 1 sur 10 20:00

[{"id":27850,"question":"Quel est le degré du polynôme P(x) = 4x³ - 2x² + 5x - 7 ?","option_a":"1","option_b":"2","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le degré d'un polynôme est l'exposant le plus élevé de la variable. Ici, l'exposant le plus élevé est 3 (pour le terme 4x³).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\", \"b\": \"2\", \"c\": \"3\", \"d\": \"4\"}}","_debug_options_count":4},{"id":27851,"question":"L'expression (x + 2)² est-elle une identité remarquable ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, c'est le carré d'une somme : (a + b)² = a² + 2ab + b². Ici, a = x et b = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":27852,"question":"Quelle est la factorisation correcte de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il s'agit d'une différence de carrés : x² - 9 = (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(x - 3)(x + 3)\", \"b\": \"(x - 9)(x + 1)\", \"c\": \"(x - 3)²\", \"d\": \"(","_debug_options_count":4},{"id":27853,"question":"L'équation x² + 4x + 4 = 0 admet-elle deux solutions distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux. Cette équation est un carré parfait : (x + 2)² = 0, donc elle admet une solution double x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":27854,"question":"Quel est le terme constant du polynôme P(x) = 3x⁴ - 5x³ + 2x - 1 ?","option_a":"3","option_b":"-5","option_c":"2","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"d","explication":"Le terme constant est le terme sans variable, ici -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"3\", \"b\": \"-5\", \"c\": \"2\", \"d\": \"-1\"}}","_debug_options_count":4},{"id":27855,"question":"La factorisation de 4x² - 16 est :","option_a":"4(x² - 4)","option_b":"4(x - 2)(x + 2)","option_c":"(2x - 4)(2x + 4)","option_d":"2(x - 2)²","option_e":"","option_f":"","bonne_reponse":"b","explication":"4x² - 16 = 4(x² - 4) = 4(x - 2)(x + 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"4(x² - 4)\", \"b\": \"4(x - 2)(x + 2)\", \"c\": \"(2x - 4)(2x + 4)\", \"d\"","_debug_options_count":4},{"id":27856,"question":"Un polynôme de degré 0 est toujours égal à :","option_a":"0","option_b":"1","option_c":"x","option_d":"une constante","option_e":"","option_f":"","bonne_reponse":"d","explication":"Un polynôme de degré 0 est une constante (ex: P(x) = 5).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"x\", \"d\": \"une constante\"}}","_debug_options_count":4},{"id":27857,"question":"L'expression 9x² + 12x + 4 est-elle factorisable ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, c'est un carré parfait : (3x + 2)² = 9x² + 12x + 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":27858,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"On factorise : x² - 5x + 6 = (x - 2)(x - 3) = 0, donc les solutions sont x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":27859,"question":"Le polynôme P(x) = x³ - 8x est-il divisible par (x - 2) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, car P(2) = 2³ - 8*2 = 8 - 16 = -8 ≠ 0 ? Erreur corrigée : P(2) = 8 - 16 = -8 ≠ 0, donc non divisible. Correction : Vrai\/Faux = Faux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]