Question

DAU COROANA
Descompuneti in factori
a) (x+1)(x+3)^2-4(x+1)
b) (x+5)(2x-1)^2-16(x+5)
c) (x-3)(x+2)^2-x+3
d) (x-4)(2x+1)^2-x+4

Answer 1

a) (x+1)(x+3)²-4(x+1) = 
       = ( x + 1) ( x² + 6x + 9 - 4) = ( x +1) · ( x² + 6x + 5 ) = 
           = ( x +1) ·( x² + x + 5x + 5) = ( x +1)·( x +1)·( x +5)   = ( x +1)²·( x +5)
b) (x+5)(2x-1)²-16(x+5) = 
       = ( x +5)· ( 4x² - 4x +1 -16) = ( x +5)· ( 4x² - 4x - 15) =
              = ( x +5) ·( 2x - 5 ) · ( 2x + 3)
c) (x-3)(x+2)²  -x+3  = 
    = ( x -3) · ( x² + 4x + 4 -1) = ( x -3) ·( x² + x + 3x + 3) = 
             = ( x -3) · ( x +1) · ( x +3) 
d) (x-4)(2x+1)² - x+4 = ( x -4) · ( 4x² + 4x + 1  -1) = 
              = ( x -4) · 4x · ( x +1)