Question

1. Rozłóż wielomiany na czynniki

a) 9x² - 25 =(3x-5(3x+5)

b)x³+2x²-9x-18

c)x⁵-4x³+x²-4

d)x³-x²-3x+3

Answer 1

a) 9x2-25=(3x-5)(3x+5)

b) x3+2x2-9x-18=x2(x+2)-9(x+2)=(x2-9)(x+2)=(x-3)(x+3)(x+2)

c) x5-4x3+x2-4=x3(x2-4)+(x2-4)=(x3+1)(x2-4)=(x3+1)(x-2)(x+2)=(x3+1^3)(x-2)(x+2)=

    = (x+1)(x2-x+1)(x-2)(x+2)

d)x3-x2-3x+3=x2(x-1)-3(x-1)=(x2-3)(x-1)=(x-pierw 3)(x+pierw 3)(x-1)

Answer 2

a) 9x² - 25 =(3x-5)(3x+5)

 

b)x³+2x²-9x-18=x²(x+2)-9(x+2)=(x+2)(x²-9)=(x+2)(x-3)(x+3)

 

c)x⁵-4x³+x²-4=x⁵+x²-4x³-4=x²(x³+1)-4(x³+1)=(x³+1)(x²-4)=(x+1)(x²-x+1)(x-2)(x+2)

 

d)x³-x²-3x+3=x²(x-1) -3(x-1)=(x-1)(x²-3)=(x-1)(x-√3)(x+√3)