Question

Rozłóż wielomiany na czynniki:

;

.

Answer 1

a)

4 x^4 - x^2 = x^2 *( 4 x^2 - 1) = x^2 *( 2x -1)*(2x + 1)

lub   4 x^4 - x^2 = x^2 *2*( x - 1/2)*2*( x + 1/2) = 4 x^2 *( x - 1/2)*( x + 1/2)

=====================================================================

b)

x^4 + x^2 - 20

Niech  t = x^2, zatem

t^2 + t - 20

delta = 1^2 - 4*1*( -20) = 1 + 80 = 81

p( delty) = 9

t1 = [ - 1 - 9]/2 = - 5

t2 = [ - 1 + 9]/2 = 4

czyli

t^2 + t - 20 = ( t + 5)*( t - 4)

zatem

x^4 + x^2 - 20 = ( x^2 + 5)*( x^2 - 4) = ( x^2 + 5)*( x - 2 )*(x + 2)

==========================================================