Phân tích đa thức thành nhân tử : a) x^4 + 5x^3 + 10x - 4 b) x^4 +y^4 +(x+y) ^4 c) (x-y)^3 + (y -z) ^3 + (z - x) ^3 d) x^4+ 7x^2 - 6x + 1
2 câu trả lời
c)(x−y)3+(y−z)3+(z−x)3=(x−y+y−z)[(x−y)2−(x−y)(y−z)+(y−z)2]−(x−z)3=(x−z)[(x−y)2−(x−y)(y−z)+(y−z)2−(x−z)2]=(x−z){[(x−y)2−(x−z)2]−[(x−y)(y−z)+(y−z)2]}=(x−z)[(x−y−x+z)(x−y+x−z)−(y−z)(x−y+y−z)]=(x−z)[(z−y)(2x+y−z)+(z−y)(x−z)]=(x−z)(z−y)(2x+y−z+x−z)=(x−z)(z−y)(3x+y−2z). Câu d em đã chép đúng đề bài chưa e?
a) x4+5x3+10x−4
=(x4−4)+(5x3+10x)
=(x2−2)(x2+2)+5x(x2+2).
b) x4+y4+[(x+y)2]2
=x4+y4+(x2+y2+2xy)2
=x4+y4+x4+y4+4x2y2+2x2y2+4x3y+4xy3
=2x4+2y4+6x2y2+4x3y+4xy3
=2(x4+y4+2x2y2)+2x2y2+4xy(x2+y2)
=2(x2+y2)2+2x2y2+4xy(x2+y2)
=2(x2+y2+xy)