Question

Calculați, vă rog !
Descompuneți in factori ireductibili polinomul :
a) 27X la puterea a 3 - 10;
b) X la puterea 8 + 3X la puterea 4 - 4;



Descompuneti in factori trinomul :
8X la puterea 2 + 3X - o,5.

Answer 1

a) 27x³-10=(3x)³-(∛10)³ =( 3x-∛10)[(9x²+3x∛10+(∛10)²]
formula a³-b³=(a-b)(a²+ab+b²)


b)x⁸+3x⁴-4=(x⁴+4)(x⁴-1)=(x⁴+4)(x²-1)(x²+1)=(x⁴+4)(x²+1)(x-1)(x+1)=
notam x⁴=a
a²+3a-4=a²+4a-a-4=a(a+4)-(a+4)=(a+4)(a-1)

c) 8x²+3x-0,5=1/2(16x²+6x-1)=1/2(16x²+8x-2x-1)=1/2[8x(2x+1)-(2x+1)]=
=1/2(2x+1)(8x-1)