Question

zad. 1 Rozłóż wielomian w na czynniki.

a) w(x)= (x+3)^2 - (2x+ 1) ^2

b) w(x)= (2x- 4)^2 - (2-x)^2

c) w(x) =5(x-1)^5- 20(x-1)^4

d) w(x)= 4(x+1)^5 - 8(x+1)^3

Answer 1

a) w(x)= (x+3)^2 - (2x+ 1) ^2 =[(x+3)-(2x+1)][(x=3)+(2x+1)]=[x+3-2x-1][x+3+2x+1]=

[-x+2][3x+4]

b) w(x)= (2x- 4)^2 - (2-x)^2=[(2x-4)-(2-x)][(2x-4)+(2-x)]=[2x-4-2+x]{2x-4+2-x]=

[3x-6][x-2]=3[x-2][x-2]

c) w(x) =5(x-1)^5- 20(x-1)^4=5(x-1)^4[x-1-4]=5(x-1)^4*(x-5)

d) w(x)= 4(x+1)^5 - 8(x+1)^3=4(x+1)^3[(x+1)^2-2]=4(x-1)^3*(x^2+2x+1-2)=

4(x-1)^3*(x^2+2x-1)=4(x-1)^3*(x+1+pierwiastek z 2)(x+1-pierwiastek z 2)