分解因式a(a^2-a-1)+13（x^2-x）^2-2(x^2-x)-8a(a^2-a-1)+13（x^2-x）^2-2(x^2-x)-8

Question

分解因式a(a^2-a-1)+1 3（x^2-x）^2-2(x^2-x)-8
a(a^2-a-1)+1

3（x^2-x）^2-2(x^2-x)-8

Answer 1

a(a²-a-1)+1
=a³-a²-a+1
=(a³-a²)-(a-1)
=a²(a-1)-(a-1)
=(a-1)(a²-1)
=(a-1)(a+1)(a-1)
=(a-1)²(a+1)
3(x²-x)²-2(x²-x)-8
=[3(x²-x)+4][(x²-x)-2]
=(3x²-3x+4)(x²-x-2)
=(3x²-3x+4)(x+1)(x-2)