Maîtrisez les polynômes : quiz interactif pour la 3ème année secondaire

Question 1 sur 10 10:00

[{"id":16128,"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},{"id":16129,"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},{"id":16130,"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},{"id":16131,"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},{"id":16132,"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},{"id":16133,"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},{"id":16134,"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},{"id":16135,"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},{"id":16136,"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},{"id":16137,"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}]