Bài 1: Phân tích đa thức thành nhân tử:
1) 8 - 12x + 6x2 - x3
2) 125x3 - 75x2 +15x -1
3) x2 - xz - 9y2 + 3xyz
4) x3 -x -5x +125
5) x3 + 2x2 - 6x - 27
6) 12x3 + 4x2 -27x - 9
7) 4x4 + 4x3 - x2 - x
8) x6 - x4 - 9x3 + 9x2
9) x4 - 4x3 + 8x2 -16x + 16
10) 3a2 - 6ab + 3b2 -12c2
11) a2 + 2ab + b2 - ac - bc
12) ac - bc - a2 + 2ab - b2
13) (x - y + 5)2 - 2(x - y + 5) + 1
14) x8 + x7 + 1
15) x8 + x4 +1
16) x5 + x + 1
17) x3 + x2 + 4
18) x4 + 2x2 - 24
19) x3 - 2x - 4
20) x2 + 4x + 3
LÀM CHI TIẾT HỘ MÌNH NHÉ !
CẢM ƠN NHÌU
1. 8 - 12x + 6x2 - x3
= 23 - 3.22.x + 3.x2.2 - x3
=(2-x)3
2. 125x3 - 75x2 +15x - 1
=(5x)3 - 3.(5x)2.1 + 3.5x.12 - 13
=(5x - 1)3
3, 4 (sai đề)
5. x3 + 2x2 - 6x - 27
=(x3 - 27) + (2x2 - 6x)
=(x3 - 33) + (2x2 - 6x)
=(x -3)(x2 + 3x + 9) + 2x(x-3)
=(x-3)(x2 + 3x +9 +2x)
=(x-3)(x2 + 5x +9)
6. 12x3 + 4x2- 27x -9
=(12x3 + 4x2) - (27x + 9)
=4x2(3x + 1) - 9(3x +1)
=(3x -1)(4x2 -9)
=(3x-1)(2x-3)(2x+3)
7) 4x3 + 4x2 - x2 - x 8) x6 - x4 - 9x3 +9x2
=(4x3 + 4x2) - (x2 - x) =x4(x2 - 1) - 9x2(x - 1)
=4x2(x + 1) - x(x+1) =x4(x-1)(x+1) - 9x2(x-1)
=(x+1)(4x2 - x) =(x-1)(x5 +x4 - 9x2)
=4x(x-1)(x+1) =x2(x-1)(x3+x2-9)
9) x4 - 4x3 + 8x2 -16x + 16 10) 3a2 - 6ab + 3b2 -12c2
=(x4 + 8x2 +16) - (4x3 + 16x) =3(a2 - 2ab + b2 - 4c2)
=(x2 + 4)2 - 4x(x2 +4) =3[(a-b)2 - (2c)2]
=(x2 + 4)(x2 +4 - 4x) =3(a-b-2c)(a-b+2c)
=(x2 + 4)(x -2)2
11) a2 + 2ab + b2 - ac - bc
= (a +b)2 -c(a+b)
=(a + b)(a + b - c)
12) ac - bc - a2 + 2ab - b2
=c(a-b) -(a-b)2
=(a-b)(c-a+b)
13) (x - y + 5)2 - 2(x - y + 5).1 + 12
=(x - y + 5 -1)2
=(x - y + 4)2
14) x8 + x7 + 1
=x8 + x7 + 1 +x2 +x - x2 - x
=(x8 - x2) + (x7 - x) + (x2 +x +1)
=x2(x6 - 1) + x(x6 - 1) + (x2 + x + 1)
=x2(x3 - 1)(x3 + 1) +x (x3 - 1)(x3 + 1) + (x2 +x +1)
=x2(x-1)(x2 + x + 1)(x3 + 1) + x(x-1)(x2 + x + 1)(x3 + 1) +(x2 + x +1)
=(x2 + x +1)[ x2(x-1)(x3 + 1) + x(x-1)(x3 +1) +1]
=(x2 + x + 1)(x6 - x4 + x3 - x +1)
15) x8 + x4 +1
=x8 + 2x4 - x4 +1
=[(x4)2 + 2.x4.1 +12] - (x2)2
=(x4 +1)2 -(x2)2
=(x4 + 1 - x2)(x4 + 1 +x2)
=(x4 - x2 +1)(x4 + 2x2 +1 - x2)
=(x4 - x2 +1)[(x2+1)2 - x2]
=(x4 - x2 +1)(x2 - x+1)(x2 +x +1)
16) x5 + x + 1
=x5 +x +1 +x2 - x2
=(x5 - x2) + (x2 + x + 1)
=x2(x3 -1) + (x2 +x +1)
=x2(x-1)(x2+x+1) + (x2+x+1)
=(x2 +x+1)(x3- x2 +1)
17) x3 + x2 + 4
=x3 + 2x2 - x2 - 2x +2x + 4
=x2(x+2) - x(x+2) +2(x+2)
=(x+2)(x2 - x +2)
18) x4 + 2x2 - 24
=(x2)2 + 2.x2.1 +12 -25
=(x2 + 1) - 52
=(x2 +1 -5)(x2 +1 +5)
=(x2- 4)(x2 +6)
=(x-2)(x+2)(x2+6)
19) x3 - 2x - 4
=x3 - 2x2 + 2x2 - 4x + 2x -4
=x2(x-2) + 2x(x-2) + 2(x-2)
=(x-2)(x2+2x+2)
20)x2 + 4x + 3
=x2 + 2.x.2 + 22 -1
=(x+2)2 -12
=(x+2-1)(x+2+1)
=(x+1)(x+3)
1)\(8-12x+6x^2-x^3\)
\(=-\left(x^3-6x^2+12x-8\right)\)
\(=-\left(x-2\right)^3\)
2)\(15x^3-75x^2+15x-1\)
\(=\left(5x-1\right)^3\)
4)
sao câu này cũng sai đề thế mắt m` lé à
giải nhanh hộ mình với mai mình phải nộp bài rồi
bạn ơi, mình xem qua có mấy cái sai đề rồi nhá, bạn xem lại rồi gửi cho mình, mình làm hết cho nếu sửa lại thì mình làm đc hết cho bạn rồi, vì nó đơn giản mà :))
