A = ( 2x + 3 )( 3x – 5 ) + ( 2x + 3 )( x – 7 )
= 6x²- 10x + 9x – 15 + 2x²- 14x + 3x - 21
= 8x² - 12x - 36
A = ( 2x + 3 )( 3x – 5 ) + ( 2x + 3 )( x – 7 )
= (2x+3)[ ( 3x-5 ) + ( x-7 ) ]
= ( 2x + 3 )( 3x – 5 + x – 7 )
= ( 2x + 3 )( 4x – 12 )
B = ( 2x + 5 )² - ( 2x + 5 )( 3x – 1 )
= 4x² + 20x + 25 – ( 6x² - 2x + 15x – 5 )
= 4x² + 20x + 25 – 6x² + 2x – 15x + 5
= - 2x² + 7x + 30
B = ( 2x + 5 )² - ( 2x + 5 )( 3x – 1 )
= ( 2x + 5 )[ ( 2x+ 5 ) – ( 3x – 1 ) ]
= ( 2x + 5 )( 2x + 5 – 3x + 1 )
= ( 2x + 5 )( - x + 6 )
C = ( 5x + 3 )( - x + 4 ) + ( 4 – x )( x – 7 )
= - 5x² + 20x – 3x + 12 + 4x – 28 – x² + 7x
= - 5x² + 17x + 12 – x² + 11x – 28
= - 6x² + 28x – 16
C = ( 5x + 3 )( - x + 4 ) + ( 4 – x )( x – 7 )
= ( 4 – x )[ ( 5x + 3 ) + ( x – 7 ) ]
= ( 4 – x )( 5x + 3 + x – 7 )
= ( 4 – x )( 6x – 4 )
D = ( 6x + 3 ) ( 4 – 5x ) – ( 4 – 5x )²
= 24x – 30x² + 12 – 15x – ( 16 – 40x + 25x²)
= 24x – 30x² - 15x + 12 – 16 + 40x – 25x²
= - 55x² + 49x – 4
D = ( 6x + 3 ) ( 4 – 5x ) – ( 4 – 5x )²
= ( 4 – 5x )[ ( 6x + 3 ) – ( 4 – 5x ) ]
= ( 4 – 5x )( 6x + 3 – 4 + 5x )
= ( 4 – 5x )( 11x – 1 )
Je calcule A si x = - 2 : A = ( 2 × (-2) + 3)( 4 × (-2) – 12 ) = - 1 × ( - 20 ) = 20
Je calcule B si x = - 2 : B = ( 2 × (-2) + 5 )( 2 + 6 ) = 1 × 8 = 8
Je calcule C si x = o : C = - 6 × 0² + 28 × 0 – 1 6 = - 16
Je calcule D si x = o : D = - 55 × 0² + 49 × 0 – 4 = - 4
EXERCICE 05 :
Je calcule la longueur de la portion en montée : 2400 × 0,4 = 960 m
La portion en montée est de 960 m
Je calcule la longueur de la portion en descente : 1/3 × 960 = 320 m
La portion en descente est de 320 m
Je calcule la longueur de la portion plate : 2400 – 320 – 960 = 1 120 m
La portion plate est de 1 120 m