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31 tháng 1 2018

a)   \(x^5-2x^4+3x^3-4x^2+2\)

\(=x^5-x^4-x^4+x^3+2x^3-2x^2-2x^2+2\)

\(=x^4\left(x-1\right)-x^3\left(x-1\right)+2x^2\left(x-1\right)-2\left(x-1\right)\left(x+1\right)\)

\(=\left(x-1\right)\left(x^4-x^3+2x^2-2x-2\right)\)

b)    \(x^4+1997x^2+1996x+1997\)

\(=\left(x^4+x^2+1\right)+1996\left(x^2+x+1\right)\)

\(=\left(x^2-x+1\right)\left(x^2+x+1\right)+1996\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+1997\right)\)

c)   \(x^8+x^4+1\)

\(=x^8+2x^4+1-x^4\)

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

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

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

c)   \(x^5+x+1\)

\(=x^5-x^2+x^2+x+1\)

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

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

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

1 tháng 10 2017

mn giúp mình vs mik đang cần gấp

29 tháng 10 2017

Bạn tự làm cho trung thực đừng dựa vào người khác

Nếu ai thấy những gì mình nói là đúng thì nhớ k nha

Thanks

10 tháng 12 2023

a) x² + 6x + 8

= x² + 2x + 4x + 8

= (x² + 2x) + (4x + 8)

= x(x + 2) + 4(x + 8)

= (x + 2)(x + 4)

b) 3x² - 2(x - y)² - 3y²

= (3x² - 3y²) - 2(x - y)²

= 3(x² - y²) - 2(x - y)²

= 3(x + y)(x - y) - 2(x - y)²

= (x - y)[3(x + y) - 2(x - y)]

= (x - y)(3x + 3y - 2x + 2y)

= (x - y)(x + 5y)

c) 4x² - 9y² + 4x - 6y

= (4x² - 9y²) + (4x - 6y)

= (2x - 3y)(2x + 3y) + 2(2x - 3y)

= (2x - 3y)(2x + 3y + 2)

d) x(x + 1)² + x(x - 5) - 5(x + 1)²

= [x(x + 1)² - 5(x + 1)²] + x(x - 5)

= (x + 1)²(x - 5) + x(x - 5)

= (x - 5)[(x + 1)² + x]

= (x - 5)(x² + 2x + 1 + x)

= (x - 5)(x² + 3x + 1)

e) 2xy - x² + 3y² - 4y + 1

= -x² + 2xy - y² + 4y² - 4y + 1

= -(x² - 2xy + y²) + (4y² - 4y + 1)

= -(x - y)² + (2y - 1)²

= (2y - 1)² - (x - y)²

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

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

f) 4x¹⁶ + 81

= (2x⁸)² + 2.2x⁸.9 + 9² - 2.2x⁸.9

= (2x⁸ + 9)² - 36x⁸

= (2x⁸ + 9) - (6x⁴)²

= (2x⁸ + 9 - 6x⁴)(2x⁸ + 9 + 6x⁴)

= (2x⁸ - 6x⁴ + 9)(2x⁸ + 6x⁴ + 9)

3 tháng 11 2018

a) x4 + 1997x2 + 1996x +1997

= x4 + 1997x2 + 1997x - x +1997

=(x4-x) + (1997x2 +1997x+1997)

=x(x3-1) + 1997(x2+x+1)

=x(x-1)(x2+x+1) + 1997(x2+x+1)

=(x2+x+1)(x2-x) + 1997(x2+x+1)

=(x2+x+1)(x2-x+1997)

b) x2 -x -2001.2002

=x2 - x -2002+2002

=(x2-20022)-(x-2002)

=(x-2002)(x+2002) - (x-2002)

=(x-2002)(x+2002+1)

=(x-2002)(x+2003)

c)x8 + 98x4 +1

= (x8+2x4+1) + 96x4

= (x4+1)2 + 96x4

=[(x4+1)2 + 2.(x4+1).8 + 64x4 ]+[32x4 - 16x2(x4+1)]

=(x4+1+8x2)-16x2(-2x2+x4+1)

=(x4+8x2+1)2- 16x2(x2-1)2

=(x4 + 8x2 +1)2- [4x(x2-1)]2

=(x4+8x2+1)2 - (4x3-4x)2

=(x4-4x3+8x2+4x+1)(x4+4x3+8x2-4x+1)

10 tháng 11 2023

a: \(P=-3x^3+5x\)

\(=x\cdot\left(-3x^2\right)+x\cdot5\)

\(=x\left(-3x^2+5\right)\)

b: \(Q=\left(2x-1\right)+\left(x-2\right)\left(2x-1\right)\)

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

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

c: \(R=4-16x^2\)

\(=4\cdot1-4\cdot4x^2\)

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

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

d: \(S=36-4x^2\)

\(=4\cdot9-4\cdot x^2\)

\(=4\left(9-x^2\right)\)

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

e: \(T=8x^3-1\)

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

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

f: \(Q=8-x^3\)

\(=2^3-x^3\)

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

g: \(N=64-x^3\)

\(=4^3-x^3\)

\(=\left(4-x\right)\left(16+4x+x^2\right)\)

20 tháng 8 2021

a) \(3xy-6xy^2=3xy\left(1-2y\right)\)

b) \(3x^3+6x^2+3x=3x\left(x^2+2x+1\right)=3x\left(x+1\right)^2\)

c) \(x^3-x^2+2\)

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

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

f) \(x^2+2x+1-9y^2=\left(x+1\right)^2-\left(3y\right)^2=\left(x-3y+1\right)\left(x+3y+1\right)\)

g) \(6x^2-12x=6x\left(x-2\right)\)

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

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

20 tháng 8 2021

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

l) \(x^3-7x^2+9x+3x^2-21x+27=x\left(x^2-7x+9\right)+3\left(x^2-7x+9\right)=\left(x+3\right)\left(x^2-7x+9\right)\)

Câu 1: A

Câu 21: A

 

1 tháng 11 2021

\(16,A\\ 17,C\\ 18,A\\ 19,C\\ 20,A\\ 21,A\)

24 tháng 6 2017

a) Ta có : x2 - 4x + 3

= x2 - x - 3x + 3

= x(x - 1) - (3x - 3) 

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

= (x - 1) (x - 3) 

24 tháng 6 2017

a) \(x^2-4x+3\)

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

\(=x\left(x-1\right)-3\left(x-1\right)\)

\(=\left(x-1\right)\left(x-3\right)\)

b) \(x^2+5x+4\)

\(=x^2+x+4x+4\)

\(=x\left(x+1\right)+4\left(x+1\right)\)

\(=\left(x+1\right)\left(x+4\right)\)

c) \(x^2-x-6\)

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

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

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

d) \(x^4+1997x^2+1996x+1997\)

\(=x^4+x^2+1996x^2+1996x+1996+1\)

\(=\left(x^4+x^2+1\right)+\left(1996x^2+1996x+1996\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+1\right)+1996\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+1997\right)\)

e) \(x^2-2001\cdot2002\)( hình như sai sai)