Răspuns:
E= (1-x)(2x³+3x+1)(2x²+2x-1)
Explicație pas cu pas:
E = 9x² - 4x⁶ - 4x³ - 1 = ?
9x² - 4x⁶ - 4x³ - 1 = 9x² - (2x³+1)²
(2x³+1)² = 4x⁶ + 4x³+1
Notam 9x² = a² si (2x³+1)² = b²
Folosim formula a²-b² = (a+b)(a-b)
=> a = √(9x²) = 3x
b = √(2x³+1)² = 2x³+1 =>
E = (3x+2x³+1)(3x-2x³-1)
E = (2x³+3x+1)(-2x³+3x-1)
Se observa ca pentru x = 1 ; -2x³+3x-1 = -2+3-1 = 0
-2x³+3x-1 se imparte exact la x-1
-2x³+3x-1 I (x-1) = -2x²-2x+1
2x³-2x²
______
/ -2x²+3x-1
2x²-2x
_____
/ x-1
-x+1
____
/ /
E = (x-1)(2x³+3x+1)(-2x²-2x+1) = (1-x)(2x³+3x+1)(2x²+2x-1)
