Question

Rozłóż wielomian na czynniki

a) w(x)=x⁴-2x²

b) w(x)=6x⁵-x⁴+x³

c) w(x)=2x⁸-2x⁷+x⁶

d) w(x)=x⁴+x³+4x²+4x

e) w(x)=2x³-2x²-x+1

Answer 1

a) w(x)=x⁴-2x²= x²(x²-2)= x²(x-√2)(x+√2)

{korzystamy z wzoru a²-b²= (a-b)*(a+b)}

b) w(x)=6x⁵-x⁴+x³= x³(6x²-x+1)

c) w(x)=2x⁸-2x⁷+x⁶= x⁶(2x²-2x+1)

d) w(x)=x⁴+x³+4x²+4x= x³(x+1)+4x(x+1)= (x+1)(x³+4x)= x(x+1)(x²+4)

e) w(x)=2x³-2x²-x+1= 2x²(x-1)-(x-1)= (x-1)(2x²-1)