Question

rozłóż wielomian na czynniki: a)P(x)= 6x(do potęgi 3) - 12x b)Q(x)= x(do potęgi 3) + 3 x (do potęgi 2) - x - 3 c)Q(x)= x(do potęgi 3) + 3x( do potęgi 2) - 4x - 12

Answer 1

a)   P(x) = 6x³-12x = 6x(x²-2) = 6x(x+√2)(x-√2)

 

b)   Q(x) = x³+3x²-x-3 = x²(x+3)-(x+3) = (x+3)(x²-1) = (x+3)(x+1)(x-1)

 

c)   q(x) = x³+3x²-4x-12 = x²(x+3)-4(x+3) = (x+3)(x²-4) = (x+3)(x+2)(x-2)

 

Answer 2

 a)P(x)= 6x³ - 12x = 6x(x²-2)=6x(x-√2)(x+√2) 

b)Q(x)= x³ + 3 x² - x - 3 = (x³-x) + (3x²-3) = x(x²-1) + 3(x²-1) = (x+3)(x²-1)=(x+3)(x-1)(x+1)

c)Q(x)= x³ + 3x² - 4x - 12 = x²(x+3) -4(x+3)=(x²-4)(x+3)=(x-2)(x+2)(x+3)

licze na naj

M