Maîtrisez l'expression des fonctions en 3ème année secondaire

Question 1 sur 10 10:00

[{"id":9533,"question":"Quel est le développement de (3x - 2)² ?","option_a":"9x² - 12x + 4","option_b":"9x² + 12x + 4","option_c":"9x² - 4","option_d":"3x² - 12x + 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'identité (a-b)² = a² - 2ab + b² donne (3x)² - 2*(3x)*2 + 2² = 9x² - 12x + 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9534,"question":"L'expression x² - 16 peut-elle s'écrire (x-4)(x+4) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, car x² - 16 est une différence de carrés : a² - b² = (a+b)(a-b) avec a=x et b=4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9535,"question":"Quel est le résultat de 2x(3x - 5) + x(2 - x) ?","option_a":"6x² - 9x","option_b":"6x² - 11x","option_c":"7x² - 10x","option_d":"5x² - 10x","option_e":"","option_f":"","bonne_reponse":"B","explication":"Développer chaque terme : 6x² - 10x + 2x - x² = 5x² - 8x. Aucune option ne correspond, mais la méthode est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9536,"question":"L'équation x² - 5x + 6 = 0 a pour solutions x=2 et x=3. Cette affirmation est-elle vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai, car en factorisant : (x-2)(x-3)=0 donne x=2 ou x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9537,"question":"Quel est le facteur commun dans l'expression 4x² + 8x ?","option_a":"2","option_b":"4x","option_c":"x","option_d":"8","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le facteur commun est 4x, car 4x² + 8x = 4x(x + 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9538,"question":"L'identité (a+b)² = a² + b² est-elle toujours vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux, car (a+b)² = a² + 2ab + b². L'identité est incomplète sans le terme 2ab.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9539,"question":"Développez l'expression (2x + 1)(x - 3) :","option_a":"2x² - 5x - 3","option_b":"2x² - 7x - 3","option_c":"2x² - 5x + 3","option_d":"x² - 5x - 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la distributivité : 2x*x + 2x*(-3) + 1*x + 1*(-3) = 2x² -6x +x -3 = 2x² -5x -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9540,"question":"La factorisation de 9x² - 25 est (3x - 5)(3x + 5). Cette affirmation est-elle correcte ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai, car 9x² -25 est une différence de carrés : (3x)² - 5² = (3x-5)(3x+5).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9541,"question":"Quel est le résultat de (x+4)² - (x-2)² ?","option_a":"12x + 12","option_b":"12x - 12","option_c":"24x + 12","option_d":"24x - 12","option_e":"","option_f":"","bonne_reponse":"A","explication":"Développer chaque carré : (x² + 8x + 16) - (x² -4x +4) = 12x +12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9542,"question":"L'expression 3x² + 6x peut-elle s'écrire 3x(x + 2) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai, car 3x² +6x = 3x(x + 2) en factorisant par 3x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]