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Clementinemaes
@Clementinemaes
April 2019
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Bonjour besoin d'aide,
a) Développer et réduire les expressions suivantes :
A (x) = (2x-3) (x²+1) - 5 (3x+2) (1-x)
B (x) = 3x + 2 - 4 (2x²+x-1) - x² (1+3x)
b) Factoriser les expressions suivantes par la méthode de votre choix
P (x) = x² - x - 1
G (x) = 3x² - 3
M (x) = (3x-2) (2-5x) - (5x+8) (3x-2)
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kvnmurty
A(x) = (2x-3)(x²+1) - 5 (3x+2)(1-x)
= 2x³ -3x² +2x - 3 - 15 x + 15 x² -10 + 10 x
= 2 x³ + 12 x² - 3 x -13 --- reduit
= (x+1) (2x² + 10 x -13) --- factorise
B(x) = 3 x + 2 - 4 (2 x² + x - 1) - x² ( 1 + 3 x)
= -3 x³ -8 x² - x² + 3x - 4x + 2 - 4
= - 3 x³ - 9 x² - x - 2 --- reduit
======================
b)
P(x) = x² - x - 1
les solutions de l'equation P(x) = 0 sont = [ +1 +- √{1+4} ] / 2
= [ 1 + √5 ]/2 et [1 - √5 ]/ 2
P(x) = [ x - (1 + √5)/2 ] [ x - (1-√5)/2 ] = [2x - 1 -√5] [ 2x - 1 +√5]/4
G(x) = 3 x² - 3 = 3 (x² - 1) = 3 (x +1 )(x - 1)
M(x) = (3x -2 )(2 - 5x) - (5x+8)(3x-2)
= (3x-2) [ (2 - 5x) - (5x+8) ]
= (3x-2) (-6 -10x)
= -2 (3x -2 ) (3+5x)
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Aidez moi sil vous plait c'est pour demain !!
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= 2x³ -3x² +2x - 3 - 15 x + 15 x² -10 + 10 x
= 2 x³ + 12 x² - 3 x -13 --- reduit
= (x+1) (2x² + 10 x -13) --- factorise
B(x) = 3 x + 2 - 4 (2 x² + x - 1) - x² ( 1 + 3 x)
= -3 x³ -8 x² - x² + 3x - 4x + 2 - 4
= - 3 x³ - 9 x² - x - 2 --- reduit
======================
b)
P(x) = x² - x - 1
les solutions de l'equation P(x) = 0 sont = [ +1 +- √{1+4} ] / 2
= [ 1 + √5 ]/2 et [1 - √5 ]/ 2
P(x) = [ x - (1 + √5)/2 ] [ x - (1-√5)/2 ] = [2x - 1 -√5] [ 2x - 1 +√5]/4
G(x) = 3 x² - 3 = 3 (x² - 1) = 3 (x +1 )(x - 1)
M(x) = (3x -2 )(2 - 5x) - (5x+8)(3x-2)
= (3x-2) [ (2 - 5x) - (5x+8) ]
= (3x-2) (-6 -10x)
= -2 (3x -2 ) (3+5x)