Bonjour,vous pouvez m'aider ? Comment on factorise 6x au carré -1x -15 ?
Mathématiques
elisa22
Question
Bonjour,vous pouvez m'aider ?
Comment on factorise 6x au carré -1x -15 ?
Comment on factorise 6x au carré -1x -15 ?
1 Réponse
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1. Réponse Anonyme
Bonjour,
[tex]6x^2 -x -15=6(x^2-\dfrac{1}{6}x-\dfrac{15}{6})\\\\6x^2 -x -15=6[(x^2-\dfrac{1}{6}x+\dfrac{1}{144})-\dfrac{1}{144}-\dfrac{15}{6}]\\\\6x^2 -x -15=6[(x-\dfrac{1}{12})^2-\dfrac{1}{144}-\dfrac{360}{144}]\\\\6x^2 -x -15=6[(x-\dfrac{1}{12})^2-\dfrac{361}{144}]\\\\6x^2 -x -15=6[(x-\dfrac{1}{12})^2-(\dfrac{19}{12})^2][/tex]
[tex]6x^2 -x -15=6[(x-\dfrac{1}{12})-\dfrac{19}{12})(x-\dfrac{1}{12})+\dfrac{19}{12})]\\\\6x^2 -x -15=6(x-\dfrac{1}{12}-\dfrac{19}{12})(x-\dfrac{1}{12}+\dfrac{19}{12})\\\\6x^2 -x -15=6(x-\dfrac{20}{12})(x+\dfrac{18}{12})\\\\6x^2 -x -15=6(x-\dfrac{5}{3})(x+\dfrac{3}{2})[/tex]