Question

因式分解:12x^4-56x^3+89x^2-56x+12

Answer 1

原式=(2x^2-5x+2)(6x^2-13x+6)
=(x-2)(2x-1)(2x-3)(3x-2)
思路么我是直接分解成(ax^2+bx+a)(cx^2+dx+c)....
或者就是x=2时原式=0,所以一定有x=2,再求解就容易多了

Answer 2

12x^4-56x^3+89x^2-56x+12
=12(x^4+1)-56x(x²+1)+89x²
=12(x²+1)²-56x(x²+1)+65x²
=[2(x²+1)-5x][6(x²+1)-13x]
=(x-2)(2x-1)(2x-3)(3x-2)