Phân tích đa thức thành nhân tử: a) 4x4+4x3-x2-x b) x6-x4-9x3+9x2 c) (xy+4)2-4(x+y)4 d) 4x4+1 e) x4+324 f) x3-x2-x-2 g) x3-9x2+6x+16 h) 6x2-11x+3 i) 2x2-5xy-3y2 k) (x+2)(x+3)(x+4)(x+5)-24 l) x2+2xy+y2-x-y-12
2 câu trả lời
a)4x4+4x3−x2−x=(4x4+4x3)−(x2+x)=4x3(x+1)−x(x+1)=x(x+1)(4x2−1)=x(x+1)(2x−1)(2x+1)
b)x6−x4−9x3+9x2=(x6−x4)−(9x3−9x2)=x4(x2−1)−9x2(x−1)=x4(x−1)(x+1)−9x2(x−1)=x2(x−1)[x2(x+1)−9]
c)(xy+4)2−4(x+y)4=(xy+4)2−[2(x+y)2]2=(xy+4−2(x+y)2)(xy+4+2(x+y)2)
d)4x4+1=4x4+4x2+1−4x2=(2x2+1)−(2x)2=(2x2+1−2x)(2x2+1+2x
)e)x4+342=x4+36x2+342−36x2=(x2+18)2−(6x)2=(x2+18−6x)(x2+18+6x)
f)x3−x2−x−2=x3−8−x2−x+6=(x3−8)−(x2+x−6)=(x−2)(x2+2x+4)−(x2−2x+3x−6)=(x−2)(x2+2x+4)−[x(x−2)+3(x−2)]=(x−2)(x2+2x+4)−(x−2)(x+3)=(x−2)(x2+2x+4−x−3)=(x−2)(x2+x+1)
dạo này mik trả lời toàn bị báo cáo thôi chẳng bt ai báo cáo nữa
a)4x4+4x3−x2−x=(4x4+4x3)−(x2+x)=4x3(x+1)−x(x+1)=x(x+1)(4x2−1)=x(x+1)(2x−1)(2x+1)b)x6−x4−9x3+9x2=(x6−x4)−(9x3−9x2)=x4(x2−1)−9x2(x−1)=x4(x−1)(x+1)−9x2(x−1)=x2(x−1)[x2(x+1)−9]c)(xy+4)2−4(x+y)4=(xy+4)2−[2(x+y)2]2=(xy+4−2(x+y)2)(xy+4+2(x+y)2)d)4x4+1=4x4+4x2+1−4x2=(2x2+1)−(2x)2=(2x2+1−2x)(2x2+1+2x)e)x4+342=x4+36x2+342−36x2=(x2+18)2−(6x)2=(x2+18−6x)(x2+18+6x)f)x3−x2−x−2=x3−8−x2−x+6=(x3−8)−(x2+x−6)=(x−2)(x2+2x+4)−(x2−2x+3x−6)=(x−2)(x2+2x+4)−[x(x−2)+3(x−2)]=(x−2)(x2+2x+4)−(x−2)(x+3)=(x−2)(x2+2x+4−x−3)=(x−2)(x2+x+1)g)x3−9x2+6x+16=x3+x2−10x2−10x+16x+16=x2(x+1)−10x(x+1)+16(x+1)=(x+1)(x2−10x+16)=(x+1)(x2−2x−8x+16)=(x+1)[x(x−2)−8(x−2)]=(x+1)(x−2)(x−8)h)6x2−11x+3=6x2−9x−2x+3=3x(2x−3)−(2x−3)=(2x−3)(3x−1)i)2x2−5xy−3y2=2x2−6xy+xy−3y2=2x(x−3y)+y(x−3y)=(x−3y)(2x+y) k)(x+2)(x+3)(x+4)(x+5)−24=(x+2)(x+5)(x+3)(x+4)−24=(x2+7x+10)(x2+7x+12)−24=(x2+7x)2+22(x2+7x)+120−24=(x2+7x)2+22(x2+7x)+96=(x2+7x)2+6(x2+7x)+16(x2+7x)+96=(x2+7x)(x2+7x+6)+16(x2+7x+6)=(x2+7x+6)(x2+7x+16)l)x2+2xy+y2−x−y−12=(x+y)2−(x+y)−12=(x+y)2−4(x+y)+3(x+y)−12=(x+y)(x+y−4)+3(x+y−4)=(x+y−4)(x+y+3)