Đáp án:
`a)(x-2)(x+3)(2x-1)(3x+1)`
`b)(x²+2x+2)(x²+5x+2)`
`c)(x²+x-5)(2x²-7x-10)`
Giải thích các bước giải:
`a)6x^4+5x³-38x²+5x+6`
`=6x^4-x³+6x³-x²-x²-36x²-x+6x+6`
`=(6x^4-x³-x²)+(6x³-x²-x)-(36x²-6x-6)`
`=x²(6x²-x-1)+x(6x²-x-1)-6(6x²-x-1)`
`=(x²+x-6)(6x²-x-1)`
`=(x²-2x+3x-6)(6x²-3x+2x-1)`
`=[x(x-2)+3(x-2)][3x(2x-1)+(2x-1)]`
`=(x-2)(x+3)(2x-1)(3x+1)`
`b)x^4+7x³+14x²+14x+4`
`=x^4+5x³+2x³+2x²+10x²+2x²+4x+10x+4`
`=(x^4+5x³+2x²)+(2x³+10x²+4x)+(2x²+10x+4)`
`=x²(x²+5x+2)+2x(x²+5x+2)+2(x²+5x+2)`
`=(x²+2x+2)(x²+5x+2)`
`c)2x^4-5x³-27x²+25x+50`
`=2x^4-7x³+2x³-10x²-7x²-10x²+35x-10x+50`
`=(2x^4-7x³-10x²)+(2x³-7x²-10x)-(10x²-35x-50)`
`=x²(2x²-7x-10)+x(2x²-7x-10)-5(x²-7x-10)`
`=(x²+x-5)(2x²-7x-10)`