A = 25x² - 80x + 64 = (5x - 8)²
B = 25x² - 64 = (5x)² - 8² = (5x - 8)(5x + 8)
C= 25x² - (2x - 3)² = (5x)² - (2x - 3)² = (5x - (2x - 3)) (5x + 2x - 3)
= (5x - 2x + 3) (7x - 3)
= (3x + 3)( 7x - 3)
= 3(x + 1)(7x - 3)
D = (8x - 1)² - 64 = (8x - 1)² - 8² = (8x - 1 - 8)(8x - 1 + 8) = (8x - 9)(8x - 7)
E = (8x - 1)² - (2x - 3)² = (8x - 1)-(2x - 3) (8x - 1 + 2x - 3)
= (8x - 1 - 2x +3)(10x - 4)
= (6x + 2)(10x - 4)
= 2(3x + 1) x 2(5x - 2)
= 4(3x +1)(5x - 2)
F = 4x² - 2x + 1 impossible a factoriser
G = (x² + 6x + 9)- (2x + 6)(x - 1) - 5(x² - 9)
G = ( x + 3)(x+3) - 2(x + 3)(x - 1) - (x - 3)(x + 3)
G = (x + 3) [(x +3) - 2(x - 1) - (x - 3)]
G = (x + 3) [ x + 3 - 2x + 2 - x + 3]
G = ( x + 3) (- 2x + 8)
G = (x + 3) -2(x - 4)
G = - 2(x + 3) ( x - 4)
3) je te laisse construire le triangle MNP
NP est le plus grand coté on a donc :
NP² = 5,3² = 28,09
MN² + MP² = 3,2² + 4² = 10,24 + 16 = 26,24
on n'a pas l'égalité de Pythagore car NP² ≠ MN² + MP² donc le triangle MNP n'est pas rectangle.
3) Dans le triangle rectangle en H
∧
cosGHE = GH / HE
cos 48° = 5/ HE
HE = 5 / cos 48°
HE = 7,47 arrondi à 10⁻¹ HE = 7,5cm
La longueur HE est de 7,5cm
