Question

Fatorando o polinômio P(x) ≡ 2x² − 7x + 3 como o produto de uma constante por polinômios de primeiro grau, teremos:


a) P(x) = 2.(x – 2) . (x + 3)

b) P(x) = 2.(x – 3).(x – ½ )

c) P(x) = (x + 2) . (x – ½ )

d) P(x) = (x – 1) . (x + 5)

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Answer 1

$P(x) = 2x^2 -7x+3 \\~\\~\\ P(x) = 2\left(x^2 -\dfrac{7x}{2}+\dfrac{3}{2}\right) \\~\\~\\ P(x) = 2\left[x^2 -\left(\dfrac{1x+6x}{2}\right)+\dfrac{3}{2}\right] \\~\\~\\ P(x) = 2\left(x^2 -\dfrac{x}{2}-\dfrac{6x}{2}+\dfrac{3}{2}\right) \\~\\~\\P(x) = 2\left(x^2 -\dfrac{x}{2}-3x+\dfrac{3}{2}\right) \\~\\~\\ P(x) = 2\left[x\left(x-\dfrac{1}{2}\right) -3\left(x-\dfrac{1}{2}\right)\right] \\~\\~\\ P(x) = 2\left(x-3\right)\left(x-\dfrac{1}{2}\right)$

Letra b) P(x) = 2.(x – 3).(x – ½ )