Question

розкласти на множники вираз (х^2+2х+3)^2-8*(х^2+2х+3)+12

Answer 1

$\displaystyle (x^2+2x+3)^2-8(x^2+2x+3)+12=\\(x^2+2x+3)^2-2(x^2+2x+3)-6(x^2+2x+3)+12=\\(x^2+2x+3)(x^2+2x+3-2)-6(x^2+2x+3-2)=(x^2+2x+3-2)(x^2+2x+3-6)=(x^2+2x+1)(x^2+3x-x-3)=(x+1)^2(x(x+3)-(x+3))=(x+1)^2(x+3)(x-1)$