Question

Rozłóż na czynniki.
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Answer 1

Odpowiedź:

b )  [tex]2 x^4 +3 x^3 -2 x^2 -3 x = 2 x^2*(x^2 - 1) + 3 x*(x^2 - 1) = (x^2 - 1)*(2 x^2 +3 x) =\\= ( x - 1)*(x + 1)*x*(2 x + 3)[/tex]

c )   [tex]8 x^4 + 24 x^3 + x + 3 = 8 x^3*(x + 3) + 1*(x + 3) = ( x + 3)*(8 x^3 + 1) =\\= ( x + 3)*(2 x + 1)*( 4 x^2 -2 x + 1 )[/tex]

e)    [tex]x^6 - 7 x^3 - 8 = ( x^3)^2 - 7 x^3 - 8 = ( x^3 + 1)*(x^3 - 8)= (x+ 1)*(x^2 - x +1)*(x -2)*(x^2 + 2x+ 4)[/tex]

f )  

256 - [tex]x^8[/tex] =  [tex]( 16 - x^4)*( 16 + x^4) = ( 4 - x^2)*(4 + x^2)*(16 + x^4) = (2 - x)*(2 + x)*(4 + x^2)*(16 + x^4)[/tex]

Szczegółowe wyjaśnienie:

[tex]a^3 + b^3 = ( a + b)*(a^2 -a*b + b^2)[/tex]

[tex]a^3 - b^3 = ( a - b)*(a^2 + a*b + b^2)[/tex]