Question

Descompuneti in factori :
a) (4x - 3)² - (2x - 1)²
b) x² + 2x - 8
c) x² - 2x - 15

Answer 1

diferenta patratelor ( 4x - 3 + 2x -1 ) ( 4x -3 - 2x +1) =( 6x -4) ( 2x-2) =
=2 ( 3x -2 ) ·2( x -1 )
 b . x² +2x  -4 -4 = x² -4  + 2x -4 = (x -2) ( x+2) + 2 ( x -2 ) = ( x -2) ·( x +4)
  c.  x² - 2x +1 -1 - 15 = ( x ² -2x +1 )  -16 = ( x -1 )²  -4² = ( x -1 -4) ·( x -1 + 4 )=
= ( x-5)· ( x +3 )

Answer 2

a) (4x - 3)² - (2x - 1)² =
= (4x - 3 - 2x + 1)(4x - 3 + 2x - 1) =
= (2x - 2)(6x - 4) =
=4 (x - 1)(3x - 2) 
b) x² + 2x - 8=(x-2)(x+4)
Δ=4+4x8=36
x₁=(-2+√36)/2=(-2+6)/2=2
x₂=(-2-√36)/2=(-2-6)/2=-4

c) x² - 2x - 15 = (x-5)(x+3)
Δ=4+4x15=64
x₁=(2+√64)/2=(2+8)/2=5
x₂=(2-√64)/2=(2-8)/2=-3