Question

1.分解因式(a-1)(a-2)(a-3)(a-4)-24

2.6x的4次方+5x³+3x²-3x-2

Answer 1

(a-1)(a-2)(a-3)(a-4)-24
=[(a-1)(a-4)][(a-2)(a-3)]-24
=(a²-5a+4)(a²-5a+6)-24
=(a²-5a+4)²+2(a²-5a+4)-24
=(a²-5a+4-4)(a²-5a+4+6)
=(a²-5a)(a²-5a+10)
=a(a-5)(a²-5a+10)

6x的4次方+5x³+3x²-3x-2
=6x的4次方+5x³+(x²+2x²)-3x-2
=(6x的4次方+5x³+x²)+(2x²-3x-2)
=x²(6x²+5x+1)+(2x+1)(x-2)
=x²(2x+1)(3x+1)+(2x+1)(x-2)
=(2x+1)(3x³+x²+x-2)
=(2x+1)(3x³-3+x²+x+1)
=(2x+1)[3(x-1)(x²+x+1)+(x²+x+1)]
=(2x+1)(3x-3+1)(x²+x+1)
=(2x+1)(3x-2)(x²+x+1)