Question

Resposta com conta ganha 20 pontos, brincadeira denunciada.
fatore: x³ - 3
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Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\sf x^3 - 3 = x^3 - (\sqrt[3]{3})^3$

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

$\sf x^3 - 3 = (x - \sqrt[3]{3}).(x^2 + (\sqrt[3]{3})x + \sqrt[3]{9})$

$\sf x^3 - 3 = x^3 + (\sqrt[3]{3})x^2 + (\sqrt[3]{9})x - (\sqrt[3]{3})x^2 - (\sqrt[3]{9})x - \sqrt[3]{27}$

$\sf x^3 - 3 = x^3 + (\sqrt[3]{3})x^2 - (\sqrt[3]{3})x^2 + (\sqrt[3]{9})x - (\sqrt[3]{9})x - \sqrt[3]{27}$

$\sf x^3 - 3 = x^3 + 0 + 0 - \sqrt[3]{27}$

$\sf x^3 - 3 = x^3 - 3$

$\boxed{\boxed{\sf x^3 - 3 = (x - \sqrt[3]{3}).(x^2 + (\sqrt[3]{3})x + \sqrt[3]{9})}}$

Answer 2

Oie, Td Bom?!

$= x {}^{3} - 3$

$= x {}^{3} - \sqrt[3]{3} {}^{ 3}$

• Fatorize a expressão usando:

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

$= (x - \sqrt[3]{3} ) \: . \: (x {}^{2} + x \sqrt[3]{3} + \sqrt[3]{3} {}^{2} )$

$= (x - \sqrt[3]{3} ) \: . \: (x {}^{2} + x \sqrt[3]{3} + \sqrt[3]{3 {}^{2} } )$

$= (x - \sqrt[3]{3} ) \: . \: (x {}^{2} + \sqrt[3]{3} x + \sqrt[3]{9} )$

Att. Makaveli1996