Question

Rozłów czynniki, stosując metodę grupowania wyrazów:

Answer 1

a) 2x³ - 3x² + 4x - 6 = x² * (2x - 3) + 2(2x - 3) = (2x -3) * ( x² + 2)

b) x³ - 5x² + 4x - 20 = x²(x - 5) + 4(x - 5) = (x - 5) * ( 4 + x²)

c) x² - 4x³ - 4x + 1 = - 4x³ - 4x + x² + 1 = -4x(x² + 1) + 1(x² +1) = (x²+1) * (1 - 4x)

d) 6x² + 3x³ + 5x + 10 = 3x²(x + 2) + 5(x + 2) = ( x + 2) * ( 5 + 3x²) 

e) 3 + 5x² - 5x³ - 3x = 5x² - 5x³ + 3 - 3x = 5x²(1 - x) + 3(1 - x) = (1 - x) * (5x² + 3)

f) 2x³ - 7x² + 2x - 7 = -7x² - 7 + 2x³ + 2x = -7(x² + 1) + 2x(x² + 1) = (x² + 1) * (2x - 7)

g) 6x² - x - x³ + 6 = 6x² + 6 - x - x³ = 6(x² + 1) - x( x² + 1) = (x² + 1) * (6 - x)

h) 5 - 2x³ + 10x² - x = 5 + 10x² - 2x³ - x = 5(1 + 2x²) - x(1 + 2x²) = (1 + 2x²) * (5 - x)