Question

Fatorando 25x elevado a 2-81 obtemos:

a) (5x-9) . (5x-9)
b) (5x+9) . ( 5x-9)
c) (5x+9) . ( 5x+9)
d) (- 5x9) . ( 5x-9)

Answer 1

$25x^2 - 81 \\ \\ \\ (5x + 9)(5x - 9)$

Resposta letra b) (5x + 9).(5x - 9)

Answer 2

Olá,

(cx+a)(cx+b) = c²x²+xb+xa+ab = 25x²-81

c²x² = 25x² 
c² = 25x²/x²
c² = 25
c =√25
c = 5

xb+xa = 0 ⇒ xb = -xa ⇒ b = -xa/x ⇒ b = -a
ab = -81
a(-a) = -81
-a² = -81
a² = 81
a = √81
a = 9

b = -a = -(9) = -9

(cx+a)(cx+b) = (5x+9)(5x-9) 

Resposta: b)