Đáp án:
Giải thích các bước giải:
1, x3−7x+6x3−7x+6
=x3−x−6x+6=x3−x−6x+6
=x(x2−1)−6(x−1)=x(x2−1)−6(x−1)
=x(x+1)(x−1)−6(x−1)=x(x+1)(x−1)−6(x−1)
=(x−1)(x2+x+6)=(x−1)(x2+x+6)
2, x3−9x2+6x+16x3−9x2+6x+16
=x3+x2−10x2−10x+16x+16=x3+x2−10x2−10x+16x+16
=(x+1)(x2−10x+16)=(x+1)(x2−10x+16)
=(x+1)(x2−2x−8x+16)=(x+1)(x2−2x−8x+16)
=(x+1)(x−2)(x−8)=(x+1)(x−2)(x−8)
3, x3−6x2−x+30x3−6x2−x+30
=x3+2x2−8x2−16x+15x+30=x3+2x2−8x2−16x+15x+30
=(x+2)(x2−8x+15)=(x+2)(x2−8x+15)
=(x+2)(x2−3x−5x+15)=(x+2)(x2−3x−5x+15)
=(x+2)(x−3)(x−5)=(x+2)(x−3)(x−5)
4, 2x3−x2+5x+32x3−x2+5x+3
=2x3+x2−2x2−x+6x+3=2x3+x2−2x2−x+6x+3
=(2x+1)(x2−x+3)=(2x+1)(x2−x+3)
5, 27x3−27x2+18x−427x3−27x2+18x−4
=27x3−9x2−18x2+6x+12x−4=27x3−9x2−18x2+6x+12x−4
=(3x−1)(9x2−6x+4)=(3x−1)(9x2−6x+4)
6, x2+2xy+y2−x−y−12x2+2xy+y2−x−y−12
=(x+y)2−(x+y)−12=(x+y)2−(x+y)−12
=(x+y)2−4(x+y)+3(x+y)−12=(x+y)2−4(x+y)+3(x+y)−12
=(x+y)(x+y−4)+3(x+y−4)=(x+y)(x+y−4)+3(x+y−4)
=(x+y−4)(x+y+3)
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