Question

Descompuneti in factori, grupand convenabil termenii:
x^6-x^4-16x^2+16=
x^3-3x^2-4x+12=
x^3+2x^2-16(x+2)=
9(2x-5)^2-4(4x-3)^2
Dau coroana! Va roog

Answer 1

x⁶-x⁴-16x²+16=x⁴(x²-1)-16(x²-1)=(x⁴-16)(x²-1)=(x²-4)(x²+4)(x-1)(x+1)=(x-2)(x+2)(x²+4)(x-1)(x+1)=(x-2)(x-1)(x+1)(x+2)(x²+4);
x³-3x²-4x+12=x²(x-3)-4(x-3)=(x²-4)(x-3)=(x-2)(x+2)(x-3)=(x-3)(x-2)(x+2);
x³+2x²-16(x+2)=x²(x+2)-16(x+2)=(x²-16)(x+2)=(x-4)(x+4)(x+2)=(x-4)(x+2)(x+4);
9(2x-5)²-4(4x-3)²=[3(2x-5)²]-[2(4x-3)]²=(6x-15)²-(8x-6)²=(6x-15-8x+6)(6x-15+8x-6)=(-2x-9)(14x-21)=7(-2x-9)(x-3);