Question

Fatore a expressão 1/2x² + 1/4x³ + 1/8x⁴

Answer 1

$(\dfrac{1}{2})x^2 + (\dfrac{1}{4})x^3 + (\dfrac{1}{8})x^4\\ \\ \\ (\dfrac{x^2}{2}) + (\dfrac{x^3}{4}) + (\dfrac{x^4}{8})\\ \\ \\ (\dfrac{x^2}{2}) + (\dfrac{x^3}{4}) + (\dfrac{x^4}{8})\\ \\ \\ (\dfrac{x^2}{2}) + (\dfrac{x^4 + 2x^3}{8})\\ \\ \\ => \dfrac{x^4 + 2x^3 + 4x^2}{8}$

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Forma fatorada: 

$x^4 + 2x^3 + 4x^2 \\ \\ \\=\ \textgreater \ x^2 (x^2 + 2x + 4)$