Question

Разложите на множители:
а) x^3+x^2-x-1
б) 16-4a+a^3-a^4

Answer 1

(x^3 + x^2) - (x + 1) = x^2( x + 1) - ( x + 1) = ( x + 1)(x^2 - 1) =
= ( x + 1)(x - 1)(x + 1) = ( x + 1)^2(x - 1)
( 16 - a^4) + ( a^3 - 4a) = (4 - a^2)(4 + a^2) + a(a^2 - 4) = -(a^2 - 4)(a^2+4)+
+ a(a^2 - 4) = ( a^2 - 4)( - a^2 + 4 +a) = - (a - 2)(a + 2)(a^2 - a - 4)