Question

Rozłóż na czynniki wielomian a) w(x) =9x^3-4x^2-27x+12 b) w(x)= 125x^3-8

Answer 1

a) w(x) =9x^3 - 4x^2 - 27x + 12 = 9x(x^2 - 3) - 4(x^2 - 3) = (9x - 4)(x^2 - 3) = (9x  -4)(x - √3)(x + √3)

 

b) w(x)= 125x^3-8 = (5x)³ - 2³ = (5x - 2)(25x² + 10x + 4)

 

a³ - b³ = (a - b)(a² + ab + b²)

Answer 2

 

a)  w(x)=9x³-4x²-27x+12=

=x²(9x-4)-3(9x-4)=

=(9x-4)(x²-3)=

=(9x-4)(x+√3)(x-√3)

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b)  w(x)=125x³-8=

=(5x)³-2³=

=(5x-2)(25x²+10x+4)

wzor:   a³-b³=(a-b)(a²+ab+b²)