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V

vipboycodon

2. x8y8+x4y4+1x^8y^8+x^4y^4+1
= x8y8+2x4y4+1−x4y4x^8y^8+2x^4y^4+1-x^4y^4
= (x4y4+1)2−(x2y2)2(x^4y^4+1)^2-(x^2y^2)^2
= (x4y4+1−x2y2)(x4y4+1+x2y2)(x^4y^4+1-x^2y^2)(x^4y^4+1+x^2y^2)
= (x4y4−x2y2+1)(x4y4+2x2y2+1−x2y2)(x^4y^4-x^2y^2+1)(x^4y^4+2x^2y^2+1-x^2y^2)
= (x4y4−x2y2+1)[(x2y2+1)2−(xy)2](x^4y^4-x^2y^2+1)[(x^2y^2+1)^2-(xy)^2]
= (x4y4−x2y2+1)(x2y2−xy+1)(x2y2+xy+1)(x^4y^4-x^2y^2+1)(x^2y^2-xy+1)(x^2y^2+xy+1)
 
C

chonhoi110

5. x3−11x2+30xx^3 - 11x^2 +30x
=x3−5x2−6x2+30x=x^3-5x^2-6x^2+30x
=x2(x−5)−6x(x−5)=x^2(x-5)-6x(x-5)
=(x2−6x)(x−5)=(x^2-6x)(x-5)
=x(x−6)(x−5)=x(x-6)(x-5)
4. x4+5x3+10x−4x^4 +5x^3 +10x - 4
=(x4+5x3−2x2)+(2x2+10x−4)=(x^4 +5x^3-2x^2)+(2x^2 +10x -4)
=x2(x2+5x−2)+2(x+5x−2)=x^2(x^2+5x-2)+2(x+5x-2)
=(x2+5x−2)(x2+2)=(x^2+5x-2)(x^2+2)
 
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C

chonhoi110

1. x4−2x3−12x2+12x+36x^4 - 2x^3 - 12x^2 +12x +36
=(x4−2x3−6x2)−(6x2−12x−36)=(x^4-2x^3-6x^2)-(6x^2-12x-36)
=x2(x2−2x−6)−6(x2−2x−6)=x^2(x^2-2x-6)-6(x^2-2x-6)
=(x2−6)(x2−2x−6)=(x^2-6)(x^2-2x-6)

3. x5+x4−x3+x2−x+2x^5 + x^4 - x^3 + x^2 - x +2
=(x5+2x4)−(x4+2x3)+(x3+2x2)−(x2+2x)+(x+2)=(x^5+2x^4)-(x^4+2x^3)+(x^3+2x^2)-(x^2+2x)+(x+2)
=x4(x+2)−x3(x+2)+x2(x+2)−x(x+2)+(x+2)=x^4(x+2)-x^3(x+2)+x^2(x+2)-x(x+2)+(x+2)
=(x+2)(x4−x3+x2−x+1)=(x+2)(x^4-x^3+x^2-x+1)
 
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