Question

Rozłóż wielomian na czynniki: a) -1/2x^6+x^5-1/2x^4 b) -6x^5+15x^4+24x^3-60x^2 c) 10x^5+15x^4-2x^2-3x d) 12x^10+24x^9-3x^8-6x^7 e) 6x^6+2x^4+x^2+1/3

Answer 1

Δ=b²-4ac

x₁=[-b-√Δ]/2a

x₂=[-b-√Δ]/2a

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a) -1/2x^6+x^5-1/2x^4=

=-1/2 x⁴(x²-2x+1)=

=-1/2 x⁴(x-1)²

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b) -6x^5+15x^4+24x^3-60x^2=

=-x⁴(6x-15)+4x²(x-15)=

=(4x²-x⁴)(6x-15)=

=x²(4-x²)(6x-15)=

=x²(2-x)(2+x)(6x-15)

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c) 10x^5+15x^4-2x^2-3x=

=5x⁴(2x+3)-x(2x+3)=

=(5x⁴-x)(2x+3)=

=x(5x³-1)(2x+3)=

=x(x∛5-1)(x²∛25-x∛5+1)(2x+3)

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d) 12x^10+24x^9-3x^8-6x^7=

12x⁹(x+2)-3x⁷(x+2)=

=(12x⁹-3x⁷)(x+2)=

=3x⁷(x²-1/4)(x+2)=

=3x⁷(x-1/2)(x+1/2)(x+2)

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e) 6x^6+2x^4+x^2+1/3

6x⁴(x²+1/3)+(x²+1/3)=

=(6x⁴+1)(x²+1/3)