Question

因式分解 在线等解答

Answer 1

1.4x^3-31x+15
=4x^3-x-30x+15
=x(4x^2-1)-15(2x-1)
=x(2x+1)(2x-1)-15(2x-1)
=(2x^2+x-15)(2x-1)
=(2x-5)(x+3)(2x-1)

2.原式=[(x^4+1)-4x^2][(x^4+1)+3x^2]+10x^4
=(x^4+1)^2-x^2(x^4+1)-12x^4+10x^4
=(x^4+1)^2-x^2(x^4+1)-2x^4
=(x^4+1-2x^2)(x^4+1+x^2)
=(x^2-1)^2[(x^4+2x^2+1)-x^2]
=(x+1)^2(x-1)^2[(x^2+1)^2-x^2]
=(x+1)^2(x-1)^2(x^2+x+1)(x^2-x+1)

追问

还有第二个。。

追答

刚打好

Answer 2

1、
4x³-31x+15
=4x(x²-9)+5x+15
=4x(x+3)(x-3)+5(x+3)
=(4x²-12x+5)(x+3)
=(2x-1)(2x-5)(x+3)
2、
(x^4-4x²+1)(x^4+3x²+1)+10x^4
=(x^4+3x²+1-7x²)(x^4+3x+1)+10x^4
=(x^4+3x²+1)²-7x²(x^4+3x+1)+10x^4
=(x^4+3x²+1-2x²)(x^4+3x²+1-5x²)
=(x^4+x²+1)(x^4-2x²+1)
=(x^4+x²+1)(x²-1)²
=(x^4+x²+1)(x-1)²(x+1)²