Quiz : Algèbre Générale — Équations, Factorisation et Identités Remarquables

Question 1 sur 10 10:00

[{"id":5795,"question":"Quel est le développement de (2x + 3)(x - 5) ?","option_a":"2x² - 7x - 15","option_b":"2x² - 13x - 15","option_c":"2x² - 10x + 3x - 15","option_d":"2x² - 7x + 15","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le développement correct est 2x² - 10x + 3x - 15 = 2x² - 7x - 15. L'option B est la simplification finale.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5796,"question":"L'équation 3x - 7 = 2x + 5 a pour solution x = 12.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En remplaçant x par 12, on obtient 3*12 - 7 = 36 - 7 = 29 et 2*12 + 5 = 24 + 5 = 29. L'équation est vérifiée, donc la solution est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5797,"question":"Quelle identité remarquable permet de factoriser x² - 16 ?","option_a":"(x - 4)²","option_b":"(x + 4)(x - 4)","option_c":"(x + 4)²","option_d":"(x - 2)(x + 8)","option_e":"","option_f":"","bonne_reponse":"B","explication":"x² - 16 est une différence de carrés : x² - 4² = (x + 4)(x - 4).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5798,"question":"La factorisation de 4x² - 20x + 25 est :","option_a":"(2x - 5)²","option_b":"(2x + 5)(2x - 5)","option_c":"(4x - 5)²","option_d":"(x - 5)(4x - 5)","option_e":"","option_f":"","bonne_reponse":"A","explication":"4x² - 20x + 25 = (2x)² - 2*2x*5 + 5² = (2x - 5)².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5799,"question":"L'inéquation 2x + 3 \u003E 7 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x ≥ 2","option_d":"x ≤ 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 3 \u003E 7 ⇒ 2x \u003E 4 ⇒ x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5800,"question":"L'expression x² + 6x + 9 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² + 6x + 9 = (x + 3)² ≥ 0 pour tout x réel. Elle est toujours positive ou nulle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5801,"question":"Quel est le résultat de (x + 2)(x - 2) - (x² - 4) ?","option_a":"0","option_b":"2x","option_c":"4","option_d":"x²","option_e":"","option_f":"","bonne_reponse":"A","explication":"(x + 2)(x - 2) = x² - 4, donc (x² - 4) - (x² - 4) = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5802,"question":"La solution de l'équation 5(x - 1) = 3x + 7 est :","option_a":"x = 6","option_b":"x = -6","option_c":"x = 2","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"5x - 5 = 3x + 7 ⇒ 2x = 12 ⇒ x = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5803,"question":"L'identité (a + b)² = a² + 2ab + b² est toujours vraie.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une identité remarquable valable pour tous nombres réels a et b.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5804,"question":"Quelle est la factorisation de x³ - 8 ?","option_a":"(x - 2)(x² + 2x + 4)","option_b":"(x - 2)³","option_c":"(x - 2)(x + 2)(x + 4)","option_d":"(x - 8)(x² + 8x + 64)","option_e":"","option_f":"","bonne_reponse":"A","explication":"x³ - 8 = (x)³ - 2³ = (x - 2)(x² + 2x + 4).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]