các bạn giúp mình với 

toan lop 8 kho qua.

\(6x^3+x^2-2x\)

=>\(x\left(6x^2+x-2\right)\)

\(e,x^2-y^2+2x+1=\left(x^2+2x+1\right)-y^2\)

\(=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)

\(f,x^3+2x^2+2x+1=\left(x^3+1\right)+\left(2x^2+2x\right)\)

\(=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-x+1+2x\right)\)

\(=\left(x+1\right)\left(x^2+x+1\right)\)

\(x^2-y^2+2x+1\)

\(=\left(x^2+2x+1\right)-y^2\)

\(=\left(x+1\right)^2-y^2\)

\(=\left(x-y+1\right)\left(x+y+1\right)\)

hk tốt

^^

c, \(2x^2+x-3=x\left(2x-3\right)\)

d, \(6x^2-x-15=x\left(6x-15\right)\)

TK MIK NHA

\(2x^2+x-3=2x^2-2x+3x-3=2x\left(x-1\right)+3\left(x-1\right)=\left(x-1\right)\left(2x+3\right) \)

a)45+x³-5x²-9x

(45-9x)+(x³-5x²)

9(5-x)+x²(x-5)

(9-x²)(5-x)

(3-x)(3+x)(5-x)

b)x⁴-2x³-2x²-2x-3

x³(x-2)-2x(x-2)-3

(x-2)(x³-2x)-3

x

a) \(x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + x - 1\)
Nhóm các hạng tử:

\(\left(\right. x^{5} - x^{4} \left.\right) + \left(\right. - 2 x^{3} + 2 x^{2} \left.\right) + \left(\right. x - 1 \left.\right) = \left(\right. x - 1 \left.\right) \left(\right. x^{4} - 2 x^{2} + 1 \left.\right) .\)

Đặt \(t = x^{2}\) thì \(x^{4} - 2 x^{2} + 1 = \left(\right. t - 1 \left.\right)^{2} = \left(\right. x^{2} - 1 \left.\right)^{2}\).
Vậy

\(\boxed{x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + x - 1 = \left(\right. x - 1 \left.\right) \left(\right. x^{2} - 1 \left.\right)^{2} = \left(\right. x - 1 \left.\right)^{3} \left(\right. x + 1 \left.\right)^{2} .}\)

b) \(x^{3} - 5 x^{2} - 14 x\)
Lấy \(x\) chung:

\(x \left(\right. x^{2} - 5 x - 14 \left.\right) = x \left(\right. x - 7 \left.\right) \left(\right. x + 2 \left.\right) .\)

\(\boxed{x^{3} - 5 x^{2} - 14 x = x \left(\right. x - 7 \left.\right) \left(\right. x + 2 \left.\right) .}\)

c) \(2 x^{2} + 2 x y - 4 y^{2}\)
Lấy \(2\) chung: \(2 \left(\right. x^{2} + x y - 2 y^{2} \left.\right)\).
Nhân tử hóa: \(x^{2} + x y - 2 y^{2} = \left(\right. x + 2 y \left.\right) \left(\right. x - y \left.\right)\).
\(\boxed{2 x^{2} + 2 x y - 4 y^{2} = 2 \left(\right. x + 2 y \left.\right) \left(\right. x - y \left.\right) .}\)

d) \(3 x^{2} + 8 x y - 3 y^{2}\)
Thử phân tích:

\(3 x^{2} + 8 x y - 3 y^{2} = \left(\right. 3 x - y \left.\right) \left(\right. x + 3 y \left.\right) .\)

\(\boxed{3 x^{2} + 8 x y - 3 y^{2} = \left(\right. 3 x - y \left.\right) \left(\right. x + 3 y \left.\right) .}\)

e) \(x^{2} - x - x y - 2 y^{2} + 2 y\)
Gộp lại theo \(x\): \(x^{2} + x \left(\right. - 1 - y \left.\right) + \left(\right. - 2 y^{2} + 2 y \left.\right)\).
Định thức là một bình phương → nghiệm \(x = 2 y\) và \(x = 1 - y\).
Vậy

\(\boxed{x^{2} - x - x y - 2 y^{2} + 2 y = \left(\right. x - 2 y \left.\right) \left(\right. x + y - 1 \left.\right) .}\)

f) \(x^{2} + 2 y^{2} - 3 x y + x - 2 y\)
Xem như phương trình bậc hai theo \(x\): nghiệm \(x = 2 y\) và \(x = y - 1\).
Do đó

\(\boxed{x^{2} + 2 y^{2} - 3 x y + x - 2 y = \left(\right. x - 2 y \left.\right) \left(\right. x - y + 1 \left.\right) .}\)

a: \(x^5-x^4-2x^3+2x^2+x-1\)

\(=x^4\left(x-1\right)-2x^2\left(x-1\right)+\left(x-1\right)\)

\(=\left(x-1\right)\left(x^4-2x^2+1\right)\)

\(=\left(x-1\right)\left(x^2-1\right)^2=\left(x-1\right)\cdot\left(x-1\right)^2\cdot\left(x+1\right)^2\)

\(=\left(x-1\right)^3\cdot\left(x+1\right)^2\)

b: \(x^3-5x^2-14x\)

\(=x\left(x^2-5x-14\right)\)

\(=x\left(x^2-7x+2x-14\right)\)

=x[x(x-7)+2(x-7)]

=x(x-7)(x+2)

c: \(2x^2+2xy-4y^2\)

\(=2\left(x^2+xy-2y^2\right)\)

\(=2\left(x^2+2xy-xy-2y^2\right)\)

=2[x(x+2y)-y(x+2y)]

=2(x+2y)(x-y)

d: \(3x^2+8xy-3y^2\)

\(=3x^2+9xy-xy-3y^2\)

=3x(x+3y)-y(x+3y)

=(x+3y)(3x-y)

e: \(x^2-x-xy-2y^2+2y\)

\(=\left(x^2-xy-2y^2\right)-\left(x-2y\right)\)

\(=\left(x^2-2xy+xy-2y^2\right)-\left(x-2y\right)\)

=x(x-2y)+y(x-2y)-(x-2y)

=(x-2y)(x+y-1)

f: \(x^2+2y^2-3xy+x-2y\)

\(=x^2-2xy-xy+2y^2+x-2y\)

=x(x-2y)-y(x-2y)+(x-2y)

=(x-2y)(x-y+1)

Đặt \(x^2-2x+4=a\)

Khi đó \(\left(x^2-2x+3\right)\left(x^2-2x+5\right)-8=\left(a-1\right)\left(a+1\right)-8\)

                                                                                    \(=a^2-1-8\)

                                                                                    \(=a^2-9\)

                                                                                      \(=\left(a-3\right)\left(a+3\right)\)

                                                                                      \(=\left(x^2-2x+4-3\right)\left(x^2-2x+4+3\right)\)

                                                                                      \(=\left(x^2-2x+1\right)\left(x^2-2x+7\right)\)

                                                                                       \(=\left(x-1\right)^2\left(x^2-2x+7\right)\)

x³ - 2x + 3

= x³ - x + 3x + 3

= x ( x² - 1 ) + 3 ( x - 1 )

= x ( x + 1 ) ( x - 1 ) + 3 ( x - 1 )

= [ x ( x + 1 ) + 3 ] ( x - 1 )

= ( x² + x + 3 ) ( x - 1 )

x³ - 2x +3

= x³ - x + 3x +3

= x ( x² - 1 ) + 3(x+1)

= x ( x+1) (x-1) +3 ( x+1)

= (x+1) ( x² - x +3 )

câu a đặt chung x ra là xong
câu b 
x^3 + 3x^2 - 7x^2 - 21x + 9x+ 27 còn lại tự làm nhé

a) x³ - 2x² + x - xy²

= x (x² - 2x + 1 - y²)

= x [(x² - 2x + 1) - y²]

= x [(x - 1)² - y²]

= x [(x - 1) + y] [(x - 1) - y]

= x (x - 1 + y) (x - 1 - y)

b) x³ - 4x² - 12x + 27

= (x³ + 27) - (4x² + 12x)

= (x³ + 3³) - 4x (x + 3)

= (x + 3) (x² - 3x + 3²) - 4x (x + 3)

= (x + 3) [(x² - 3x + 9) - 4x]

= (x + 3) (x² - 3x + 9 - 4x)

= (x + 3) (x² - 7x + 9)

#Học tôt!!!

~NTTH~