Exercices de factorisation
a(x) =−3x+ 6 b(x) =−5x−10 c(x) = 7x−21
d(x) = 3ab−5a2c−7a3b e(x) = 7abc−8bc+ 21abe f(x) =−3xy+ 10yz−13yt g(x) = 3a2c−15ab2+ 21a2b2c h(x) =−7x2y+ 35xz2−28xyz2 i(x) = 5xyz−10xz2+ 30yz j(x) = 2a2b2c−6bc2+ 10abc3 k(x) =−5x2yz+ 35xz2−40x2y2z2 l(x) = 3a2bc+ 15a3b2d−39a2bc m(x) = (2x+5)(3x−1)−(3x−7)(3x−1) n(x) = (−5x+ 4)(−2x−5) + (−7x+ 4)(−4x−10)
o(x) = (2x−3)(4x−7)−(3x−9)(−4x+7) p(x) = (−3x−7)(2x−5) + 4x2−25 q(x) = (−5x− 10)(3x− 5) + (2x+ 4)(−3x−7)
r(x) = (−3x−9)(−3x+ 7) + 5(x2−9) s(x) = (−2x+ 4)(−3x+ 7) + 5(x−2)2 t(x) = 4x2+ 4x+ 1
u(x) = 9x2−6x+ 1 v(x) = 49x2−25y2 w(x) = 2x2−4x+ 2
x(x) =−(x−3)2+ (3x−8)2 y(x) = (2x−7)2−25(x−8)2 z(x) =−16(x−5)2+ 36(3x−2)2
Parcours 1
A1= (2x+ 1)(3x+ 5) + (4x+ 2)(2x+ 1) B1= (x−2)(x+ 3) + (x−2)(4x−1) C1= (5x−3)(2x−5)−x(5x−3) D1= (x+ 1)(x+ 3)−5(x+ 3) E1= (x+ 4)(x−2) + (3x+ 1)(x+ 4) F1= (x−3)(2x+ 1) + (2x+ 1)(3x−2) G1= (3x+ 2)(7x−1)−10(7x−1) H1= 2(6x−7) + (6x−7)(x+ 3) I1=−7(3x−7)(−2x−7)+5(3x−7)(x+
3)
Parcours 2 A2= 64x2−49 B2= 16x2−40x+ 25 C2=t2+ 12t+ 36 D2=y2−81 E2= 9x2−24x+ 16 F2=x2+ 14x+ 49 G2= 100t2−121 H2= 9x2−6x+ 1 I2= 49x2−42x+ 9 J2= 64x2−81 Parcours 3
A3= (7x+ 3)(3x−2) + 3x−2 B3= 8x−5−(8x+ 1)(8x−5) C3= 3(3x−7)2−3x+ 7 D3= (6x−1)(7x−3) + 7x−3 E3= 6x+ 1 + (6x+ 1)(x−5) F3= (3x+ 2)(7x−1)−7x+ 1 G3= (x−3)(2x+ 1) + 2x+ 1 H3= (x+ 4)(x−2)−x−4 I3= 3−7x−(x+ 4)(7x−3) Parcours 4
A4= (2x−1)(3x+ 5) + (4x+ 2)(1−2x) B4= (x−2)(x+ 3) + (2−x)(4x−1) C4= (5x−3)(2x−5)−x(3−5x) D4= (x+ 1)(x−3)−5(3−x) E4= (x−4)(x−2) + (3x+ 1)(4−x) F4= (x−3)(2x−1) + (1−2x)(3x−2) G4= (3x+ 2)(7x−1)−10(1−7x) H4= 2(6x−7) + (7−6x)(x+ 3) I4=−7(−3x−4) + (−7−6x)(3x+ 4) J4=−5(−3x−9) + 3x(x+ 3) + (−7− 6x)(2x+ 6)
K4 = −3(6x−21) + 3x(−4x+ 14)− (−7−6x)(−2x+ 7)
Parcours 5
A5= 9x2−16 + (3x+ 4)(3x−2) B5= (4x−1)2−(x−5)2
C5= (7x−5)(3x+ 2)−6(3x+ 2)(x+ 3) D5= (2x+ 3)(2x−1) + 4x2+ 12x+ 9 E5= (x+ 4)(−2x+ 1)−3(x+ 4)2 F5=x2−9−(2x+ 5)(x−3) + 5x−15 G5= 4x2−9 + (2x+ 3)(x−5)
H5= (2x+ 7)2+ 10x+ 35 I5=x2−16 + (x+ 4)2 Parcours 6
A6= 9x2−5x B6= 6x+ 9
C6=x(x+ 5) +x(3x−2)
D6= (x+ 4)(x−6) + (−1 +x)(x−6) E6= (3x−1)−(3x−1)2
F6=x2+ 8x+ 16 G6= 4−x2
H6= 9x2−30x+ 25 I6= 25−36x2 J6= (4x−3)2−1 Parcours 7
A7= (2x+ 1)2−(4x+ 2)(2x+ 1) B7= (x−2)2+ (x−2)(4x−1) C7= (5x−3)2−x(5x−3) D7= (x+ 1)(x+ 3)−(x+ 3)2 E7= 5(x+ 4)2−(3x+ 1)(x+ 4) F7= (x−3)(2x+ 1)−7(2x+ 1)2 G7= (7x−1)2−10(7x−1) H7= 2(6x−7)−7(6x−7)2
I7=−5(2x−5)2−7(2x−5)(x+ 3) Parcours 8
A8 = (2x+ 1)(3x+ 5)−(6x+ 3)(2x+ 1)−(−1−2x)2
B8= (x−2)(x+ 3)−7(x2−4)−(−5x+ 10)(−3x+ 7)
C8= (5x−3)(2x−5)−7x(−15x+ 9)− 7(3−5x)
D8 = (x+ 1)(−6−2x)−5(x+ 3) + 5(3x+ 9)2
E8=−7(x+ 4)(x−2) + 8x2−32−(4− 2x)(−x−7)
F8 =−3(x−3)(2x+ 1) + (4x+ 2)2− 5(3x−2)(−3−6x)
G8= (−3x+ 2)(7x−1)−10(−7x+ 1)− 3(−7x+ 1)2
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