Mathématiques

Question

bonjour pouvez vous m'aider a factoriser les exercices suivants merci d'avance !
bonjour pouvez vous m'aider a factoriser les exercices suivants merci d'avance !

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2 Réponse

  • A) 9x*-(x-1)*= (3x)* -(x-1)*= (3x-x+1) (3x+x-1) = (2x+1)(4x-1)

    B) (3x-2)* -4(x-1)* = 9x*-12x +4 - 4 ( x*+2x+1) = 9x*-12x+4-4x*-8x-4 =5x* -4x = x(5x-4)

    C) (2x-5)+(4x+3) - (5x-3)(2x-5) = (2x-5)(4x+3-5x+3) = (2x-5)(-x+6)

    D) (5x-4)(1-2x) -(1-2x) = (1-2x)(5x-4-1) =( 1-2x)(5x-5)

    E) (6x-1)*- (6x-1) = (6x-1)(6x-1-1) =(6x-1)(6x-2)

    F) (3-5x)*+ x (3-5x) -2(5x-3) = (3-5x) (3-5x+x+2) = (3-5x)(-4x+5)

  • Factoriser les expressions suivantes

    A(x) = 9 x² - (x - 1)² ⇔ A = (3 x)² - (x - 1)² c'est une identité remarquable de la forme a² - b² = (a + b)(a - b)

    a² = (3 x)² ⇒ a = 3 x

    b² = (x - 1)² ⇒ b = (x - 1)

    A(x) = (3 x)² - (x - 1)² = (3 x + x - 1)(3 x - x + 1)

    = (4 x - 1)(2 x + 1)

    B(x) = (3 x - 2)² - 4(x - 1)² ⇔ B(x) = (3 x - 2)² - (2(x - 1))² identité remarquable identique que ci-dessus

    B(x) = (3 x - 2)² - (2(x - 1))² = (3 x - 2 + 2(x - 1))(3 x - 2 - 2(x - 1))

    B(x) = (3 x - 2 + 2x - 2))(3 x - 2 - 2x + 2))

    B(x) = x(5 x - 4)

    C(x) = (2 x - 5)(4 x + 3) - (5 x - 3)(2 x - 5)

    = (2 x - 5)(4 x + 3 - 5 x + 3)

    = (2 x - 5)(6 - x)

    D(x) = (5 x - 4)(1 - 2 x) - (1 - 2 x)

    = (1 - 2 x)(5 x - 4 - 1)

    = (1 - 2 x)(5 x - 5)

    = 5(1 - 2 x)(x - 1)

    E (x) = (6 x - 1)² - (6 x - 1)

    = (6 x - 1)(6 x - 1 - 1)

    = (6 x - 1)(6 x - 2)

    = 2(6 x - 1)(3 x - 1)

    F (x) = (3 - 5 x)² + x(3 - 5 x) - 2(5 x - 3)

    ⇔F (x) = (3 - 5 x)² + x(3 - 5 x) - 2(- (3 - 5 x))

    ⇔F (x) = (3 - 5 x)² + x(3 - 5 x) + 2(3 - 5 x)

    = (3 - 5 x)(3 - 5 x + x + 2)

    = (3 - 5 x)(5 - 4 x)


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