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

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

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

=x(x^3+1)(x-1)(x^2+x+1)+(x^2+x+1)

=[(x^4+x)(x-1)+1](x^2+x+1)

=(x^5-x^4+x^2-x)(x^2+x+1)

24 tháng 8 2021

Trả lời:

1, x7 + x2 + 1 

= x7 + x2 + 1 + x6 - x6 + x5 - x5 + x4 - x4 + x3 - x3 + x2 - x2 + x - x 

= ( x7 + x6 + x5 ) - ( x6 + x5 + x4 ) + ( x4 + x3 + x2 ) - ( x3 + x2 + x ) + ( x2 + x + 1 )

= x5 ( x2 + x + 1 ) - x( x2 + x + 1 ) + x2 ( x2 + x + 1 ) - x ( x2 + x + 1 ) + ( x2 + x + 1 )

= ( x2 + x + 1 )( x5 - x4 + x2 - x + 1 )

b, x8 + x7 + 1 

= x8 + x7 + 1 + x6 - x6 + x5 - x5 + x4 - x4 + x3 - x3 + x2 - x2 + x - x 

= ( x8 + x7 + x6 ) - ( x6 + x5 + x4 ) + ( x5 + x4 + x3 ) - ( x3 + x2 + x ) + ( x2 + x + 1 ) 

= x6 ( x2 + x + 1 ) - x4 ( x2 + x + 1 ) + x3 ( x2 + x + 1 ) - x ( x2 + x + 1 ) + ( x2 + x + 1 )

= ( x2 + x + 1 )( x6 - x4 + x- x + 1 )

26 tháng 10 2018

       \(x^4-3x^2+9\)

\(=\left(x^2\right)^2+2.x^2.3+3^2-9x^2\)

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

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

       \(x^4+3x^2+4\)

\(=\left(x^2\right)^2+2.x^2.2+2^2-x^2\)

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

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

15 tháng 10 2017

\(=x^4+1999x^2-x+1999x+1999\)

\(=\left(x^4-x\right)+\left(1999x^2+1999x+1999\right)\)

\(=x\left(x^3-1\right)+1999\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+1999\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+1999\right)\)

9 tháng 8 2021

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

2, \(x^2+3x-10=x^2+5x-2x-10=x\left(x-2\right)+5\left(x-2\right)=\left(x+5\right)\left(x-2\right)\)

3, \(x^2-x-12=x^2-4x+3x-12=x\left(x+3\right)-4\left(x+3\right)=\left(x-4\right)\left(x+3\right)\)

4, \(3x^2+4x-7=3x^2+7x-3x-7=3x\left(x-1\right)+7\left(x-1\right)=\left(3x+7\right)\left(x-1\right)\)

5, \(4x^2-9y^2-5xy=4x^2-9xy+4xy-9y^2\)

\(=4x\left(x+y\right)-9y\left(x+y\right)=\left(4x-9y\right)\left(x+y\right)\)

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

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