Odpowiedź:
a) x³ + 3x² - 4x – 12=x²(x+3)-4(x+3)=(x+3)(x²-4)=(x+3)(x+2)(x-2)
b) 7x³ + 2x² - 21x – 6=x²(7x+2)-3(7x+2)=(x²-3)(7x+2)=(x+✓3)(x-✓3)(7x+2)
c) 9x³ - 4x² - 27x + 12=x²(9x-4)-3(9x-4)=(x²-3)(9x-4)=(x+✓3)(x-✓3)(9x-4)
d) x³ - x² + x – 1=x²(x-1)+(x-1)=(x²+1)(x-1)
e) 4x³ + 4x² - x – 1=4x²(x+1)-(x+1)=(x²-1)(x+1)=(x-1)((x+1)(x+1)=(x-1)(x+1)²
f) 3x³ - 6x² + 4x – 8=3x²(x-2)+4(x-2)=(3x²+4)(x+2)
g) 5x³ - 4x² - 5x + 4=5x(x²-1)-4(x²-1)=(5x-4)(x²-1)=(5x-4)(x+1)(x-1)
h) 16x³ + 16x² - 4x – 4=16x²(x+1)-4(x+1)=(16x²-4)(x+1)=(4x+2)(4x-2)(x+1)
i) 3x³ - 7x² - 27x + 63=3x(x²-9)-7(x²-9)=(3x-7)(x²-9)=(3x-7)(x-3)(x+3)
j) 10x³ + 15x² + 8x + 12=5x²(2x+3)+4(2x+3)=(5x²+4)(2x+3)
