Question

Escreva a forma fatorada dos polinômios.
f) 1/5x² - 4/5x + 4/5 =
Respostas completas, para hoje!!

Answer 1

$\begin{aligned}&\qquad~~~\dfrac{1}{5}x^2-\dfrac{4}{5}x+\dfrac{4}{5}~~\Longleftrightarrow\\\\&\Longleftrightarrow~~\dfrac{1}{5}x^2-\dfrac{1}{5}\cdot4x+\dfrac{1}{5}\cdot4~~\Longleftrightarrow\\\\&\Longleftrightarrow~~\dfrac{1}{5}(x^2-4x+4)~~\Longleftrightarrow\\\\&\Longleftrightarrow~~\boxed{\dfrac{1}{5}(x-2)^2}~~~~~~\big[\because~(x-2)^2=x^2-2\cdot x\cdot 2+2^2=x^2-4x+4\big].\end{aligned}$

Ou seja, 1/5 (x - 2)² é a forma fatorada de 1/5x² - 4/5x + 4/5.