Ảnh 1
Bài 1
a) x^2 + 4x + 3
= ( x + 1 ).( x + 3 )
d) 2x^2 + 3x - 5
= ( x - 1 ).( 2x + 5 )
b) 16x - 5x^2 - 3
= ( 3 - x )( 5x - 1 )
c) 2x^2 + 7x + 5
= ( 2x + 1 ).( 2x + 5 )
e) x^3 - 3x^2 + 1 - 3x
= ( x + 1 ).( x^2 - 4x + 1 )
f) x^2 - 4x - 5
= ( x + 1 ).( x - 5 )
h) x^3 - 3x^2 - 4x + 12
= x^2.( x - 3 ) - 4.( x - 3 )
= ( x - 3 ).( x + 2 ).( x - 2 )
Nếu đúng hãy cho mình + và 5 sao nha >.<

IV chia đa thức:Vấn đề III
Bài 4
a, x^3 - x^2 - 14x + 24
= x^3 - 2x^2 +x^2 - 2x - 12x +24
= (x-2)(x^2 + x - 12)
= (x-2)(x-3)(x+4)

b, x^3 + 4x^2 + 4x + 3
= x^3 + 3x^2 + x^2 + 3x + x + 3
= (x+3)(x^2 + x + 1)

c, x^3 - 7x - 6
= x^3 + x^2 - x^2 - x - 6x - 6
= (x+1)(x^2 - x - 6)
= (x+1)(x+2)(x-3)

d, x^3 - 19x - 30
= x^3 - 5x^2 + 5x^2 - 25x + 6x - 30
= (x-5)(x^2 + 5x + 6)
= (x-5)(x+2)(x+3)

e, a^3 - 6a^2 + 11a - 6
= a^3 - a^2 - 5a^2 + 5a + 6a - 6
= (a-1)(a^2 - 5a + 6)
= (a-1)(a-2)(a-3)

IV. chia đa thức: Vấn đề 2
Bài 3
a, (5x^2 + 9xy - 2y^2) : (x+2y)
= (5x^2 + 10xy - xy - 2y^2) : (x+2y)
= [5x(x+2y) - y(x+2y)] : (x+2y)
= (x+2y)(5x-y) : (x+2y)
= 5x-y
b, (x^4 - x^3.y + x^2.y^2 - xy^3) : (x^2 + y^2)
= x(x^3 - y^3 - x^2.y + x.y^2) : (x^2 + y^2)
= x[(x-y)(x^2 + xy + y^2) - xy(x-y)] : (x^2 + y^2)
= x(x-y)(x^2 + xy + y^2 - xy)
= x(x-y)(x^2 + y^2) : (x^2 + y^2)
= x(x-y)
= x^2 - xy

IV. chia đa thức: Vấn đề 2
Bài 2:
a, (2x^4 - 5x^2 + x^3 - 3 - 3x) : (x^2 - 3)
= (2x^4 - 6x^2 + x^3 - 3x + x^2 - 3) : (x^2 - 3)
= (x^2 - 3)(2x^2 + x + 1) : (x^2 - 3)
= 2x^2 + x + 1

b, (x^5 + x^3 + x^2 + 1) : (x^3 + 1)
= (x^5 + x^2 + x^3 + 1) : (x^3 + 1)
= (x^3 + 1)(x^2 + 1) : (x^3 + 1)
= x^2 + 1

IV. chia đa thức: Vấn đề 2
Bài 2:
c, (2x^3 + 5x^2 - 2x + 3) : (2x^2 - x + 1)
= (2x^3 - x^2 + x + 6x^2 - 3x + 3) : (2x^2 - x + 1)
= (2x^2 - x + 1)(x+3) : (2x^2 - x + 1)
= x+3

d, (8x - 8x^3 - 10x^2 + 3x^4 - 5) : (3x^2 - 2x + 1)
= (3x^4 - 2x^3 + x^2 - 6x^3 + 4x^2 - 2x - 15x^2 + 10x - 5) : (3x^2 - 2x + 1)
= (3x^2 - 2x + 1)(x^2 - 2x - 5) : (3x^2 - 2x + 1)
= x^2 - 2x - 5

Bài 7
a, (x^2 + 4x + 8)^2 + 3x(x^2 + 4x + 8) + 2x^2
Đặt x^2 + 4x + 8) = y
ta có:
y^2 + 3xy + 2x^2
= y^2 + xy + 2xy + 2x^2
= (x+y)(2x+y)
= (x+ x^2 + 4x + 8)(2x + x^2 + 4x + 8)
= (x^2 + 5x + 8)(x^2 + 6x + 8)
= (x^2 + 5x + 8)(x+2)(x+4)
b, (x^2 + x + 1)(x^2 + x + 2) - 12
Đặt x^2 + x + 2 = y
ta có:
(y-1).y - 12
= y^2 - y - 12
= (y+3)(y-4)
= (x^2 + x + 2 + 3)(x^2 + x + 2 - 4)
= (x^2 + x + 5)(x^2 + x - 2)

Bài 7
c, (x^2 + 8x + 7)(x^2 + 8x + 15) + 15
Đặt x^2 + 8x + 11 = y
ta có :
(y-4)(y+4) + 15
= y^2 - 16 + 15
= y^2 - 1
= (y-1)(y+1)
= (x^2 + 8x + 11 - 1)(x^2 + 8x + 11 + 1)
= (x^2 + 8x + 10)(x^2 + 8x + 12)
= (x^2 + 8x + 10)(x+2)(x+6)
d, (x+2)(x+3)(x+4)(x+5) - 24
= (x+2)(x+5)(x+3)(x+4) - 24
= (x^2 + 7x+ 10)(x^2 + 7x + 12) - 24
Đặt x^2 + 7x + 11 = y
ta có:
(y-1)(y+1) - 24
= y^2 - 1 - 24
= y^2 - 25
= (y-5)(y+5)
= (x^2 + 7x + 11 - 5)(x^2 + 7x + 11 + 5)
= (x^2 + 7x + 6)(x^2 + 7x + 16)
= (x+1)(x+6)(x^2 + 7x + 16)

Vấn đề V. Tổng hợp
Bài 1
a, x^2 + 4x + 3
= x^2 + x + 3x + 3
= x(x+1) + 3(x+1)
= (x+1)(x+3)
d, 2x^2 + 3x - 5
= 2x^2 - 2x + 5x - 5
= 2x(x-1) + 5(x-1)
= (x-1)(2x+5)
g, (a^2 + 1)^2 - 4a^2
= (a^2 + 1 + 2a)(a^2 + 1 - 2a)
= (a+1)^2.(a-1)^2

Vấn đề V. Tổng hợp
Bài 1
b, 16x - 5x^2 - 3
= -5x^2 + 15x + x - 3
= -5x(x-3) + (x-3)
= (x-3)(1-5x)
e, x^3 - 3x^2 + 1 - 3x
= (x^3 + 1) + (-3x^2 - 3x)
= (x+1)(x^2 - x + 1) - 3x(x+1)
= (x+1)(x^2 - x - 3x + 1)
= (x+1)(x^2 - 4x + 1)
h, x^3 - 3x^2 - 4x + 12
= x^2.(x-3) - 4(x-3)
= (x-3)(x^2 - 4)
= (x-3)(x-2)(x+2)

Vấn đề V. Tổng hợp
Bài 1
c, 2x^2 + 7x + 5
= 2x^2 + 2x + 5x + 5
= 2x(x+1) + 5(x+1)
= (x+1)(2x+5)
f, x^2 - 4x - 5
= x^2 + x - 5x - 5
= x(x+1) - 5(x+1)
= (x+1)(x-5)
i, x^4 + x^3 + x + 1
= x^3.(x+1) + (x+1)
= (x+1)(x^3 + 1)
= (x+1)^2.(x^2 - x + 1)

Vấn đề V. Tổng hợp
Bài 1
k, x^4 - x^3 - x^2 + 1
= x^3.(x-1) - (x^2 - 1)
= x^3.(x-1) - (x-1)(x+1)
= (x-1)(x^3 - x - 1)
l, (2x+1)^2 - (x-1)^2
= (2x+1-x+1)(2x+1+x-1)
= (x+2)3x
= 3x(x+2)
m, x^4 + 4x^2 - 5
= x^4 + 4x^2 + 4 - 9
= (x^2 + 2)^2 - 9
= (x^2 + 2 - 3)(x^2 + 2 + 3)
= (x^2 - 1)(x^2 + 5)
= (x-1)(x+1)(x^2 + 5)

Vấn đề V. Tổng hợp
Bài 2
a, -x - y^2 + x^2 - y
= -(x+y) + (x^2 - y^2)
= -(x+y) + (x-y)(x+y)
= (x+y)(x-y-1)
d, 5x^3 - 5x^2.y - 10x^2 + 10xy
= 5x(x^2 - xy - 2x + 2y)
= 5x[x(x-y) - 2(x-y)]
= 5x(x-y)(x-2)
g, x^2 - y^2 - 2xy + y^2
= x^2 - 2xy
= x(x-2y)

Vấn đề V. Tổng hợp
Bài 2
b, x(x+y) - 5x - 5y
= x(x+y) - 5(x+y)
= (x+y)(x-5)
e, 27x^3 - 8y^3
= (3x-2y)(9x^2 + 6xy + 4y^2)
h, x^2 - y^2 + 4 - 4x
= (x^2 - 4x + 4) - y^2
= (x-2)^2 - y^2
= (x-2-y)(x-2+y)

Vấn đề V. Tổng hợp
Bài 2
c, x^2 - 5x + 5y - y^2
= (x^2 - y^2) - 5(x-y)
= (x-y)(x+y) - 5(x-y)
= (x-y)(x+y-5)
f, x^2 - y^2 - x - y
= (x-y)(x+y) - (x+y)
= (x+y)(x-y-1)
i, x^6 - y^6
= (x^3 - y^3)(x^3 + y^3)
= (x-y)(x^2 + xy + y^2)(x+y)(x^2 - xy + y^2)

Vấn đề V. Tổng hợp
Bài 2
k, x^3 + 3x^2 + 3x + 1 - 27z^3
= (x+1)^3 - 27z^3
= (x+1-3z)[(x+1)^2 + 3z(x+1) + 9z^2)
= (x+1-3z)(x^2 + 2x + 1 - 3zx + 3z + 9z^2)
l, 4x^2 + 4x - 9y^2 + 1
= (4x^2 + 4x + 1) - 9y^2
= (2x+1)^2 - 9y^2
= (2x+1-3y)(2x+1+3y)
m, x^2 - 3x + xy - 3y
= (x^2 + xy) - (3x + 3y)
= x(x+y) - 3(x+y)
= (x+y)(x-3)

Vấn đề V. Tổng hợp
Bài 3
a, 5x^2 - 10xy + 5y^2 - 20z^2
= 5(x^2 - 2xy + y^2 - 4z^2)
= 5[(x-y)^2 - 4z^2]
= 5(x-y-2z)(x-y+2z)
d, x^2 - 2xy + 2yz - z^2
= (x^2 - z^2) - (2xy - 2yz)
= (x-z)(x+z) - 2y(x-z)
= (x-z)(x+z-2y)
g, x^2 - y^2 + 2yz - z^2
= x^2 - (y^2 - 2yz + z^2)
= x^2 - (y-z)^2
= (x-y+z)(z+y-z)
 

Vấn đề V. Tổng hợp
Bài 3
b, x^2 - z^2 + y^2 - 2xy
= (x^2 - 2xy + y^2) - z^2
= (x-y)^2 - z^2
= (x-y-z)(x-y+z)
e, 3x^2 - 6xy + 3y^2 - 12z^2
= 3(x^2 - 2xy + y^2 - 4z^2)
= 3[(x-y)^2 - 4z^2]
= 3(x-y-z)(x-y+z)
h, x^2 - 2xy + y^2 - xz + yz
= (x-y)^2 - z(x-y)
= (x-y)(x-y-z)
 

Vấn đề V. Tổng hợp
Bài 3
c, a^3 - ay - a^2.x + xy
= (a^3 - a^2.x) - (ay-xy)
= a^2.(a-x) - y(a-x)
= (a-x)(a^2 - y)
f, x^2 - 6xy - 25z^2 + 9y^2
= (x^2 - 6xy + 9y^2) - 25z^2
= (x-3y)^2 - 25z2
= (x-3y+5z)(x-3y-5z)
i, x^2 - 2xy + tx - 2ty
= (x^2 + tx) - (2xy + 2ty)
= x(x+t) - 2y(x+t)
= (x+t)(x-2y)

Vấn đề V. Tổng hợp
Bài 3
k, 2xy + 3z + 6y + xz
= (2xy+xz) + (3z+6y)
= x(2y+z) + 3(z+2y)
= (x+3)(2y+z)
l, x^2 + 2xz + 2xy + 4yz
= x(x+2z) + 2y(x+2z)
= (x+2z)(x+2y)
m, (x+y+z)^3 - x^3 - y^3 - z^3
= (x+y+z-x)[(x+y+z)^2 + x(x+y+z) + x^2) - (y+z)(y^2 - yz + z^2)
= (y+z)(x^2 + y^2 + z^2 + 2xy + 2xz + 2yz + x^2 + xy + xz + x^2 - y^2 - z^2 + yz)
= (y+z)(3x^2 + 3xy + 3xz + 3yz)
= 3(y+z)(x^2 + xy + xz + yz)

Vấn đề V. Tổng hợp
Bài 4
a, x^3 + x^2.z + y^2.z - xyz + y^3
= (x^3 + y^3) + z(x^2 - xy + y^2)
= (x+y)(x^2 - xy + y^2) + z(x^2 - xy + y^2)
= (x+y+z)(x^2 - xy + y^2)
b, bc(b+c) + ca(c-a) - ab(a+b)
= bc(b+c) + ca(b+c-a-b) - ab(a+b)
= bc(b+c) + ac(b+c) - ac(a+b) - ab(a+b)
= (b+c)(bc+ac) - (a+b)(ac+ab)
= c(b+c)(a+b) - a(a+b)(b+c)
= (a+b)(b+c)(c-a)
d, a^6 - a^4 + 2a^3 + 2a^2
= (a^3 + a^2)(a^3 - a^2) + 2(a^3 + a^2)
= (a^3 + a^2)(a^3 - a^2 + 2)
= a^2.(a+1)(a^3 - a^2 + 2)

Vấn đề V. Tổng hợp
Bài 4
e, x^9 - x^7 - x^6 - x^5 + x^4 + x^3 + x^2 - 1
= x^7.(x^2 - 1) - x^4.(x^2 - 1) - x^3.(x^2 - 1) + (x^2 - 1)
= (x^2 - 1)(x^7 - x^4 - x^3 + 1)
= (x-1)(x+1)[x^4.(x^3 - 1) - (x^3 - 1)]
= (x-1)(x+1)(x^3 - 1)(x^4 - 1)
= (x-1)(x+1)(x-1)(x^2 + x + 1)(x^2 - 1)(x^2 + 1)
= (x-1)^3.(x+1)^2.(x^2 + x + 1)(x^2 + 1)
f, (x+y+z)^3 - x^3 - y^3 - z^3
= (x+y+z-x)[(x+y+z)^2 + x(x+y+z) + x^2) - (y+z)(y^2 - yz + z^2)
= (y+z)(x^2 + y^2 + z^2 + 2xy + 2xz + 2yz + x^2 + xy + xz + x^2 - y^2 - z^2 + yz)
= (y+z)(3x^2 + 3xy + 3xz + 3yz)
= 3(y+z)(x^2 + xy + xz + yz)
h, x^3 + y^3 + z^3 - 3xyz
= x^3 + 3x^2.y + 3xy^2 + y^3 + z^3 - 3xyz - 3x^2.y - 3xy^2
= (x+y)^3 + z^3 - 3xy(z+x+y)
= (x+y+z)[(x+y)^2 - z(x+y) + z^2] - 3xy(x+y+z)
= (x+y+z)(x^2 + 2xy + y^2 - xz - yz + z^2 - 3xy)
= (x+y+z)(x^2 + y^2 + z^2 - xy - xz - yz)

Ảnh 1, Bài đầu:
a, (x^2 + x)^2 - 14(x^2 + x) + 24
Đặt x^2 + x = y
ta có:
y^2 - 14y + 24
= y^2 - 2y - 12y + 24
= (y-2)(y-12)
= (x^2 + x - 2)(x^2 + x - 12)
= (x^2 + x - 2)(x-3)(x+4)
b, (x^2 + x)^2 + 4x^2 + 4x - 12
= (x^2 + x)^2 + 4(x^2 + x) - 12
Đặt x^2 + x = y
ta có :
y^2 + 4y - 12
= y^2 - 2y + 6y - 12
= y(y-2) + 6(y-2)
= (y-2)(y+6)
= (x^2 + x - 2)(x^2 + x + 6)

Ảnh 1, Bài đầu:
c, x^4 + 2x^3 + 5x^2 + 4x - 12
= x^4 - x^3 + 3x^3 - 3x^2 + 8x^2 - 8x + 12x - 12
= (x-1)(x^3 + 3x^2 + 8x + 12)
= (x-1)(x^3 + 2x^2 + x^2 + 2x + 6x + 12)
= (x-1)[x^2.(x+2) + x(x+2) + 6(x+2)]
= (x-1)(x+2)(x^2 + x + 6)
d, (x+1)(x+2)(x+3)(x+4) + 1
= (x+1)(x+4)(x+2)(x+3) + 1
= (x^2 + 5x + 4)(x^2 + 5x + 6) + 1
Đặt x^2 + 5x + 5 = y
ta có:
(y-1)(y+1) + 1
= y^2 - 1 + 1
= y^2
= (x^2 + 5x + 5)^2

Ảnh 1, Bài đầu:
e, (x+1)(x+3)(x+5)(x+7) + 15
= (x+1)(x+7)(x+3)(x+5) + 15
= (x^2 + 8x + 7)(x^2 + 8x + 15) + 15
Đặt x^2 + 8x + 11 = y
ta có :
(y-4)(y+4) + 15
= y^2 - 16 + 15
= y^2 - 1
= (y-1)(y+1)
= (x^2 + 8x + 11 - 1)(x^2 + 8x + 11 + 1)
= (x^2 + 8x + 10)(x^2 + 8x + 12)
= (x^2 + 8x + 10)(x+2)(x+6)
f, (x+1)(x+2)(x+3)(x+4) - 24
= (x+1)(x+4)(x+2)(x+3) - 24
= (x^2 + 5x + 4)(x^2 + 5x + 6) - 24
Đặt x^2 + 5x + 5 = y
ta có:
(y-1)(y+1) - 24
= y^2 - 1 - 24
= y^2 - 25
= (y-5)(y+5)
= (x^2 + 5x + 5 - 5)(x^2 + 5x + 5 + 5)
= (x^2 + 5x)(x^2 + 5x + 10)
= x(x+5)(x^2 + 5x + 10)

Vấn đề V. Tổng hợp
Bài 5
a, (x-2)^2 - (x-3)(x+3) = 6
<=> x^2 - 4x + 4 - x^2 + 9 = 6
<=> -4x = 6 - 13
<=> -4x = -7
<=> x = 7/4
b, (x+3)^2 + (4+x)(4-x) = 10
<=> x^2 + 6x + 9 + 16 - x^2 = 10
<=> 6x + 25 = 10
<=> 6x = 10 - 25
<=> 6x = -15
<=> x = -15/6
<=> x = -5/2

Vấn đề V. Tổng hợp
Bài 5
c, (x+4)^2 + (1-x)(1+x) = 7
<=> x^2 + 8x + 16 + 1 - x^2 = 7
<=> 8x + 17 = 7
<=> 8x = 7 - 17
<=> 8x = -10
<=> x = -10/8
<=> x = -5/4
d, (x-4)^2 - (x-2)(x+2) = 6
<=> x^2 - 8x + 16 - x^2 + 4 = 6
<=> -8x + 20 = 6
<=> -8x = 6-20
<=> -8x = -14
<=> x = 14/8
<=> x = 7/4

Vấn đề V. Tổng hợp
Bài 5
e, 4(x-3)^2 - (2x-1)(2x+1) = 10
<=> 4(x^2 - 6x + 9) - (4x^2 - 1) = 0
<=> 4x^2 - 24x + 36 - 4x^2 + 1 = 0
<=> -24x + 37 = 0
<=> -24x = -37
<=> x = 37/24
f, 25(x+3)^2 + (1-5x)(1+5x) = 8
<=> 25(x^2 + 6x + 9) + 1 - 25x^2 = 8
<=> 25x^2 + 150x + 225 + 1 - 25x^2 = 8
<=> 150x + 226 = 8
<=> 150x = 8 - 226
<=> 150x = -218
<=> x = -218/150
<=> x = -109/75

IV. Chia đa thức . VĐ1
bài 1
a, (-2)^5 : (-2)^3
= (-2)^2
= 4
b, (-y)^7 : (-y)^3
= (-y)^4
= y^4
c, x^12 : (-x)^10
= x^12 : x^10
= x^2
d, (2x)^6 : (2x)^3
= (2x)^3
= 8x^3

IV. Chia đa thức . VĐ1
Bài 2
a, (x+2)^9 : (x+2)^6
= (x+2)^3
= x^3 + 6x^2 + 12x + 8
Bài 1
e, (-3x)^5 : (-3x)^2
= (-3x)^3
= -27x^3
f, (xy^2)^4 : (xy^2)^2
= (xy^2)^2
= x^2.y^4

IV. Chia đa thức . VĐ1
Bài 3
a, 6xy^2 : 3y
= 2xy
b, 6x^2.y^3 : 2xy^2
= 3xy
c, 8x^2.y : 2xy
= 4x
d, 5x^2.y^5 : xy^3
= 5xy^2

IV. Chia đa thức . VĐ1
Bài 3
e, (-4x^4.y^3) : 2x^2.y
= -2x^2.y^2
f, xy^3.z^4 : (-2xz^3)
= -y^3.z/2
h, 9x^2.y^4.z : 12xy^3
= 3xyz/4
i, (2x^3.y)(3xy^2) : 2x^3.y^2
= 2x^4.y^3 : 2x^3.y^2
= xy

Vấn đề V. Tổng hợp
Bài 6
a, a^2.(a+1) + 2a(a+1)
= (a+1)(a^2 + 2a)
= a(a+1)(a+2)
Vi a; a+1; a+2 là ba số liên tiếp mà tích của 3 số liên tiếp luôn chia hết 6
=> a(a+1)(a+2) chia hết 6
Vậy a^2.(a+1) + 2a(a+1) chia hết 6
b, a(2a-3) - 2a(a+1)
= a(2a-3) - a(2a+2)
= a(2a-3-2a-2)
= a(-5)
= -5a
Vì -5 chia hết cho 5
=> -5a chia hết 5
Vậy a(2a-3) - 2a(a+1) chia hết 5

Vấn đề V. Tổng hợp
Bài 6
c, x^2 + 2x + 2
= x^2 + 2x + 1 + 1
= (x+1)^2 + 1
Vì (x+1)^2  ≥ 0
     1 > 0
=> (x+1)^2 + 1 > 0
=> x^2 + 2x + 2 > 0

d, -x^2 + 4x - 5
= -(x^2 - 4x + 4) - 1
= -(x-2)^2 - 1
Vì -(x-2)^2 ≤ 0
        -1 < 0
=> -(x-2)^2 - 1 < 0
=> -x^2 + 4x - 5 < 0 

Vấn đề III
Bài 4
a, x^3 - x^2 - 14x + 24
= x^3 - 2x^2 + x^2 - 2x - 12x + 24
= x^2.(x-2) + x(x-2) - 12(x-2)
= (x-2)(x^2 + x - 12)
= (x-2)(x^2 - 3x + 4x - 12)
= (x-2)(x-3)(x+4)

b, x^3 + 4x^2 + 4x + 3
= x^3 + 3x^2 + x^2 + 3x + x + 3
= x^2.(x+3) + x(x+3) + (x+3)
= (x+3)(x^2 + x + 1)

Vấn đề III
Bài 4
c, x^3 - 7x - 6
= x^3 - x - 6x - 6
= x(x^2 - 1) - 6(x+1)
= x(x-1)(x+1) - 6(x+1)
= (x+1)(x^2 - x - 6)
= (x+1)(x+2)(x-3)

d, x^3 - 19x - 30
= x^3 - 4x - 15x - 30
= x(x^2 - 4) - 15(x+2)
= x(x-2)(x+2) - 15(x+2)
= (x+2)(x^2 - 2x - 15)
= (x+2)(x+3)(x-5)

e, a^3 - 6a^2 + 11a - 6
= a^3 - a^2 - 5a^2 + 5a + 6a - 6
= a^2.(a-1) - 5a(a-1) + 6(a-1)
= (a-1)(a^2 - 5a + 6)
= (a-1)(a-2)(a-3)