1) Factoriser A=4x²-12x+9 puis B=4x²-12x+9+(2x-3)(3x-1) 2Reprendre la question prècèdente avec : a) C= x²+2x+1 et D=x²+2x+1-8x(x+1) b) E= 16+8x+x² et F=(x+16)(x

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1/_
A=4x*-12x+9
A=(2x-3)*
A=(2x-3)(2x-3)

B=4x*-12x+9+(2x-3)(3x-1)
B=A+(2x-3)(3x-1)
B=(2x-3)(2x-3)+(2x-3)(3x-1)
B=(2x-3)[(2x-3)+(3x-1)]
B=(2x-3)[2x-3+3x-1]
B=(2x-3)(5x-4)

2/_

a) C=x*+2x+1 et D=x*+2x+1-8x(x+1)
C=(x+1)*
C=(x+1)(x+1)

Et D= C -8x(x+1)
D=(x+1)(x+1)-8x(x+1)
D=(x+1)[(x+1)-8x]
D=(x+1)[x+1-8x]
D=(x+1)(-7x+1)

b) E=16+8x+x* et F=(x+16)(x+4)-(x*+8x+16)
E=(x+4)*
E=(x+4)(x+4)
et F=(x+16)(x+4)-E
F=(x+16)(x+4)-(x+4)(x+4)
F=(x+4)[(x+16)-(x+4)]
F=(x+4)(x+16-x-4)
F=(x+4)(12)
F=12(x+4)

c) G=25x*-9 et H=(5x+3)(5x+9)-(25x*-9)
G=25x*-(3)* identité remarquable
G=(5x-3)(5x+3)
et H=(5x+3)(5x+9)-(25x*-9)
H=(5x+3)(5x+9)-G
H=(5x+3)(5x+9)-(5x-3)(5x+3)
H=(5x+3)[(5x+9)-(5x-3)]
H=(5x+3)(5x+9-5x+3)
H=(5x+3)(12)
H=12(5x+3)