Question

Descompuneti in factori ireductibili polinomul:
8X^3-(X-5)^3.


Prin acest semn ^ indicatoare la ce putere este

Answer 1

$8x^3 =2^3x^3=(2x)^3$

 Pentru  $8x^3-(x-5)^3$  se foloseste formula diferentei cuburilor:

$a^3-b^3=(a-b)(a^2+ab+b^2)$

Answer 2

    
[tex]8x^3 - (x-5)^3 = 2^3x^3 - (x-5)^3 =(2x)^3 - (x-5)^3 \\ Folosim ~formula: \\ a^3-b^3=(a-b)(a^2+ab+b^2) \\ \\ \bold{(2x)^3 - (x-5)^3} = [2x-(x-5)][(2x)^2 +2x(x-5) + (x-5)^2]= \\ = [2x-x+5][4x^2 +2x^2-10x + x^2 -10x +25]= \\ = \boxed{(x+5)(7x^2 -20x +25)}[/tex]