Question

$3x^{6}-4x^{5}+2x^{4} - 8x^{3} +2x^{2}-4x+3=0$ . разложить на множители

Answer 1

$3x^{6}-4x^{5}+2x^{4} - 8x^{3} +2x^{2}-4x+3=3x^{4}(x^2+1)-4x^3(x^2+1)-x^2(x^2+\\+1)-4x(x^2+1)+3(x^2+1)=(x^2+1)(3x^4-4x^3-x^2-4x+3)=(x^2+\\+1)(3x^2(x^2+x+1)-7x(x^2+x+1)+3(x^2+x+1))=(x^2+1)(x^2+x+\\+1)(3x^2-7x+3)$