Question

Rozłóż czynniki na wielomiany:

a) 3t²(2t-5)-9(6t-15)

b) (x²-9)(x²-6x+9)

Answer 1

a)

3t²(2t-5)-9*3(2t-5)=(2t-5)(3t²-27)=3(t²-9)(2t-5)=3(t+3)(t-3)(2t-5)

Wielomian

(t²-9)(2t-5)=2t³-5t²-18t+45

b)

(x+3)(x-3)(x-3)²=(x-3)³(x+3)

Wielomian

x^4-6x³+9x²-9x²+54x-81=x^4-6x³+54x-81

Answer 2

a)

3t²(2t-5) - 9(6t-15 = 3t²(2t-5) - 9*3(2t-5) = (3t²-9*3)(2t-5) = 3(t²-9)(2t-5) = 3(t+3)(t-3)(2t-5)

Wielomian:

3(t+3)(t-3)(2t-5) = 3(t²-9)(2t-5) = 3(2t³-5t²-18t+45) = 6t³-15t²-54t+135

 

b)

(x²-9)(x²-6x+9) = (x+3)(x-3)(x-3)² = (x+3)(x-3)³

        x²-6x+9 = 0

        Δ = 36-36 = 0

         x = 6/2 = 3

Wielomian:

(x+3)(x-3)³ = (x+3)(x³-9x²+27x-27) = x⁴-9x³+27x²-27x+3x²-27x²+87x-87 = x⁴-6x³+54x-81