Question

21. descompuneti in factori

a) (x+2)³- 4(x+2)
b) (x-3)³- 9(x-3)
c) (x-7)³ -16(x-7)
d) (1-4x)³- 25( 1-4x)
e) (4-3x)³+ 49(3x-4)
f) (1-5x)³+ 36(5x-1)
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Answer 1

Răspuns:

a) (x+2)³- 4(x+2)=(x+2)(x^2+4x+4-4)=

=x(x+2)(x+4)

b) (x-3)³- 9(x-3)=(x-3)(x^2-6x+9-9)=

=x(x-3)(x-6)

c) (x-7)³ -16(x-7)=(x-7)(x^2-14x+49-16)

(x-7)(x^2-14+33)

d) (1-4x)³- 25( 1-4x) =(1-4x)(1-8x+16x^2-25)=

( 1-4x)(16x^2-8x-24)

e) (4-3x)³+ 49(3x-4)=

= (4-3x)(16-24x+9x^2-49)=

=(4-3x)(9x^2-24x-33)

f) (1-5x)³+ 36(5x-1)=(1-5x)(1-10x+25x^2-36)=

=(1-5x)(25x^2-10x-35)=

=5(1-5x)(5x^2-2x-7)

Answer 2

Răspuns:

Explicație pas cu pas:

$a) x^3+3x^2*2+3x*2^2+2^3-4x-8=x^3+6x^2+12x+8-4x-8=\\=x^3+6x^2+8x=x(x^2+6x+8)\\\\b) x^3-9x^2+27x-27-9x+27=x^3-9x^2+18x\\c) x^3-21x^2+147x-49-16x+112=x^3+21x^2+131x+63\\d)(4x-1)^3+25(4x-1)=64x^3-12x^2+8x-1+100x-25=\\64x^3-12x^2+108x-26\\e) (3x-4)^3-49(-3x+4)=27x^3-36x^2-64+147x-4=\\27x^3-36x^2+147x-68\\f) (5x-1)^3-36(-5x+1)=125x^3-15x^2+15x-1+180x-36=\\125x^3-15x^2+195x-37$