Question

1. rozłóż na czynniki wielomiany metodą grupowania wyrazów:
w(x) = x³-3x+2
w(x) = x³+4x-5
2. rozłóż na czynniki wielomiany:
w(x) =x⁴-10x²+9
w(x) =-3x⁴+2x²+1
w(x) = x⁴-18x²+81
w(x) =(x²-3x)²-9x²


Najlepiej zrobione zostanie nagrodzone ! Na odpowiedzi czekam do dziś do 20

Answer 1

1.w(x)=x²(x-3) +2
w(x)=x²(x+4)-5
2.w(x)=x²(x²-10)+9
w(x)=x²(-3x²+2)+1
w(x)=x²(1-18)+81
w(x)=(x²)²+6x³-9x² -9x²=(x²)²+6x³-18x²=x²(x²+6x-18)

Answer 2

W(x) = x³-3x+2=x3-x - 2x + 2=x(x2-1)-2(x-1)=x(x-1)(x+1) - 2(x-1)= (x-1)[x(x+1)-2]=(x-1)(x2+x-2)

w(x) = x³+4x-5=x3 -1x+5x-5=x(x2-1)+5(x-1)=x(x-1)(x+1)+5(x-1)=
(x-1)(x(x+1)+5)=(x-1)(x2+x+5)

w(x) =x⁴-10x²+9
x2=t
W(X)=t2-10t+9
delta=100-36=64 pierwiastek z delty=8
t1=(10-8)/2=2/2=1
t2=(10+8)/2=18/2=9
W(x)=(t-1)(t-9)=(x2-1)(x2-9)=(x-1)(x+1)(x-3)(x+3)

w(x) =-3x⁴+2x²+1
x2=t
w(x)=-3t2+2t+1
delta=4+12=16 pier z delty=4
t1=(-2-4)/(-6)=-6/(-6)=1
t2(-2+4)/(-6)=2/(-6)=-1/3
W(x)=-3(t-1)(t+1/3)=-3(x2-1)(x2+1/3)=-3(x+1)(x-1)(x2+1/3)

w(x) = x⁴-18x²+81
x2=t
w(x)=t2-18t+81
delta=324-324=0
t0=18/2=9
w(x)=(t-9)2=(x2-9)2=(x-3)2(x+3)2

w(x) =(x²-3x)²-9x²=x4-6x3+9x2-9x2=x4-6x3=x3(x-6)