Quiz — كثيرات الحدود.pdf

Question 1 sur 10 20:00

[{"id":41955,"question":"Quel est le degré du polynôme P(x) = 3x⁴ - 2x³ + 5x - 7 ?","option_a":"1","option_b":"3","option_c":"4","option_d":"5","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le degré d'un polynôme est l'exposant le plus élevé de la variable x. Ici, c'est 4.","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\": \"3\", \"c\": \"4\", \"d\": \"5\"}}","_debug_options_count":4},{"id":41956,"question":"L'identité remarquable (a - b)² est égale à :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'identité (a - b)² = a² - 2ab + b² est correcte.","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":41957,"question":"Factorisez l'expression x² - 9 :","option_a":"(x - 3)(x - 3)","option_b":"(x - 3)(x + 3)","option_c":"(x + 3)(x + 3)","option_d":"x(x - 9)","option_e":"","option_f":"","bonne_reponse":"b","explication":"x² - 9 est une différence de carrés : (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\": \"b\", \"options\": {\"a\": \"(x - 3)(x - 3)\", \"b\": \"(x - 3)(x + 3)\", \"c\": \"(x + 3)(x + 3)\", \"d","_debug_options_count":4},{"id":41958,"question":"La division euclidienne de P(x) = x³ + 2x² - 5x + 1 par D(x) = x - 1 donne un reste égal à :","option_a":"0","option_b":"1","option_c":"2","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant le théorème du reste, P(1) = 1 + 2 - 5 + 1 = -1. Le reste est donc -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"-1\"}}","_debug_options_count":4},{"id":41959,"question":"L'équation x² + 5x + 6 = 0 a pour solutions :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Les solutions sont x = -2 et x = -3, donc l'affirmation est fausse.","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":41960,"question":"Quel est le coefficient dominant du polynôme 4x³ - 2x² + x - 5 ?","option_a":"4","option_b":"-2","option_c":"1","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient dominant est le coefficient du terme de plus haut degré, ici 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\": \"4\", \"b\": \"-2\", \"c\": \"1\", \"d\": \"-5\"}}","_debug_options_count":4},{"id":41961,"question":"Factorisez l'expression 2x² + 8x :","option_a":"2x(x + 4)","option_b":"x(2x + 8)","option_c":"(2x + 4)(x)","option_d":"2(x² + 4x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x² + 8x = 2x(x + 4) par mise en facteur commun.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2x(x + 4)\", \"b\": \"x(2x + 8)\", \"c\": \"(2x + 4)(x)\", \"d\": \"2(x² + 4","_debug_options_count":4},{"id":41962,"question":"La somme de deux polynômes de degré 3 est toujours de degré 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Si les termes de degré 3 s'annulent, le degré peut être inférieur à 3.","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":41963,"question":"Résolvez l'inéquation x² - 4x + 3 \u003E 0 :","option_a":"x \u003C 1 ou x \u003E 3","option_b":"1 \u003C x \u003C 3","option_c":"x \u003C 3","option_d":"x \u003E 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les racines sont x=1 et x=3. Le polynôme est positif à l'extérieur de l'intervalle [1,3].","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 \u003C 1 ou x \u003E 3\", \"b\": \"1 \u003C x \u003C 3\", \"c\": \"x \u003C 3\", \"d\": \"x \u003E 1\"}}","_debug_options_count":4},{"id":41964,"question":"Quel est le reste de la division de x⁴ + 2x³ - x + 1 par x² + x ?","option_a":"x + 1","option_b":"-x + 1","option_c":"2x + 1","option_d":"x - 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"En effectuant la division, le reste est -x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x + 1\", \"b\": \"-x + 1\", \"c\": \"2x + 1\", \"d\": \"x - 1\"}}","_debug_options_count":4}]