Quiz : Testez vos connaissances sur les polynômes !

Question 1 sur 10 10:00

[{"id":41576,"question":"Quel est le degré du polynôme P(x) = 3x⁴ - 2x³ + 5x - 7 ?","option_a":"4","option_b":"3","option_c":"5","option_d":"2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le degré d'un polynôme est le plus haut exposant de x avec un coefficient non nul. Ici, c'est x⁴, donc le degré est 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41577,"question":"L'identité remarquable (a - b)² est égale à :","option_a":"a² - 2ab + b²","option_b":"a² + 2ab + b²","option_c":"a² - b²","option_d":"a² + b²","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'identité (a - b)² se développe en a² - 2ab + b², c'est une formule à connaître par cœur.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41578,"question":"Un polynôme du second degré admet toujours deux racines réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. Un polynôme du second degré peut avoir deux racines réelles distinctes, une racine double (racine unique) ou aucune racine réelle (discriminant négatif).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41579,"question":"Factorisez : 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":"x² - 9 est une différence de carrés, donc factorisable en (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41580,"question":"Le polynôme P(x) = x³ - 2x² - x + 2 admet x = 1 comme racine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. En substituant x = 1 dans P(x), on obtient 1 - 2 - 1 + 2 = 0, donc 1 est bien une racine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41581,"question":"Quelle est la forme factorisée de P(x) = x² + 4x + 4 ?","option_a":"(x + 2)²","option_b":"(x - 2)²","option_c":"(x + 4)(x + 1)","option_d":"(x - 4)(x - 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² + 4x + 4 est un carré parfait, donc factorisable en (x + 2)².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41582,"question":"Un polynôme de degré 3 peut avoir au maximum 3 racines réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. Un polynôme de degré n peut avoir au maximum n racines réelles (en comptant les multiplicités).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41583,"question":"Développez : (2x - 1)(x + 3).","option_a":"2x² + 5x - 3","option_b":"2x² + 7x - 3","option_c":"2x² - 5x - 3","option_d":"2x² + x - 3","option_e":"","option_f":"","bonne_reponse":"B","explication":"En développant (2x - 1)(x + 3), on obtient 2x² + 6x - x - 3 = 2x² + 5x - 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41584,"question":"Le polynôme P(x) = x³ - x est factorisable par :","option_a":"x","option_b":"x - 1","option_c":"x + 1","option_d":"x² + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"P(x) = x(x² - 1) = x(x - 1)(x + 1), donc il est factorisable par x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41585,"question":"L'équation x² + 2x + 5 = 0 admet deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. Le discriminant Δ = 4 - 20 = -16 est négatif, donc l'équation n'admet pas de solution réelle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]