Question

Rozłóż wyrażenuie na czynniki:

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

znowu matma:(

Answer 1

a)=[(x^2 - 5) -4[](x^2 - 5)+4]=[x^2 - 9][x^2 - 1]=(x-3)(x+3)(x-1)(x+1) wzor a^2-b^2=(a-b)(a+b)

b)=[(x^2 + 1)-2x][(x^2 +1) +2x]=(x^2-2x+1)(x^2+2x+1)=(x-1)^2(x+1)^2  

wzor a^2-2ab+b^2=(a-b)^2  wzor a^2+2ab+b^2=(a+b)^2

c)=[6-x(x-5)][6+x(x-5)]=[-x^2+5x+6][x^2-5x+6]

delta1=25-4(-1)6=49                          delta2=25-4(1)(6)=1

x1=6                                                             x1=2

x2=-1                                                            x2=3

= - (x-6)(x+1)(x-2)(x-3)

d)

=[x^2-x-1-x^2}[x^2-x-1+x^2}=(-x-2)(2x^2-x-1)=-(x+1)2(x-1)(x+1/2)= -2(x+1)(x-1)(x+1/2)

e)

=[x^3+x^2-1-(2x^2-3)]=[x^3+x^2-1+(2x^2-3)]=[x^3-x^2+2][x^3+3x^2-4] to rozkladajac(*)

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

 

(x^2-2x+2) nie rozklada sie delta<0

 

x^3+3x^2-4=x^3-x^2+4x^2-4=x^2(x-1)+4(x-1)=(x-1)(x^2+4)

 

(*)=(x+1)(x^2-2x+2)(x-1)(x^2+4)

uff

f)=[3-(x^2-4)][3+(x^2-4)]=(7-x^2)(x^2-1)=(\/7 - x)(\/7 + x)((x - 1)(x + 1)

g)= [x^2+1/4- x][x^2+1/4 +x]=(x-1/2)^2(x+1/2)^2

h)=[x^2+3 - 4x][x^2+3+4x]=(x-1)(x-3)(x+1)(x+3)   widać ze x=1 (-1) mz drugi ze wzorow viete'a

i)=[x-(x^2+x+1)[x+(x^2+x+1)]=(-x^2-1)(x^2+2x+1)= - (x^2+1)(x+1)^2 wzory skr

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

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

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