Question

Rozłóz wielomian w na czynniki .
a) w(x)=12^5-3x^3
b) w(x)= 2x^5+16x^2
c) w(x)=3x^5-6x^4-6x^3
d)w(x)=4x^4+8x^3+12x^2

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Answer 1

a) w(x)=12x^5-3x^3=3x³(4x²-1)=3x³(2x+1)(2x-1)
b) w(x)= 2x^5+16x^2=2x²(x³+8)=2x²((x+2)(x²-2x+4)
c) w(x)=3x^5-6x^4-6x^3=3x³(x²-2x-2)=3x³(x-1+√3)(x-1-√3) bo;
      Δ=4+8=12          √Δ=2√3    x1=[2-2√3]2=1-√3    x2=[1+√3
d)w(x)=4x^4+8x^3+12x^2=4x²(x²+2x+3)