\(x^4+2008x^2+2007x+2008\\ =x^4-x+2008\left(x^2+x+1\right)=x\left(x^3-1\right)+2008\left(x^2+x+1\right)=x\left(x-1\right)\left(x^2+x+1\right)+2008\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(x^2-x+2008\right)\)

Ta có: \(x^4+2008x^2+2007x+2008\)

\(=x^4-x+2008\left(x^2+x+1\right)\)

\(=x\left(x^3-1\right)+2008\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+2008\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2008\right)\)

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  x^4 + 2008x^2 + 2007x + 2008

\(=x^4+x^2+2007x^2+2007x+2007+1\)

\(=x^4+x^2+1+2007\left(x^2+x+1\right)\)

\(=\left(x^2+1\right)^2-x^2+2007\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+1\right)+2007\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2008\right)\)

2x^4 hay x^4

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

b: \(x^8+x^7+1\)

\(=x^8+x^7+x^6-x^6-x^5-x^4+x^5+x^4+x^3-x^3-x^2-x+x^2+x+1\)

\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)

c: \(x^8+x^4+1\)

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

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

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

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

\(a)\; x^4+4 \\= x^4+4x^2+4-4x^2\\=(x^2+2)^2-4x^2\\=(x^2+2-2x)(x^2+2+2x)\)

x^4+2008x^2+2007x+2008

=x^4+2008x^2+2008x-x+2008

=(x^4-x)+(2008x^2+2008x+2008)

=x(x^3-1)+2008(x^2+x+1)

=x(x-1)(x^2+x+1)+2008(x^2+x+1)

=(x^2+x+1)(x^2-x+2008)

       x⁴+2008x²+2007x+2008

<=> x⁴-x+2008x²+2008x+2008

<=> x(x³-1)+2008(x²+x+1)

<=> x(x-1)(x²+x+1)+2008(x²+x+1)

<=> (x²+x+1)(x²-x+2008)

\(\left(x^4+x^2+1\right)+\left(2007x^2+2007x+2007\right)\)

=\(\left(x^2+x+1\right)\left(x^2-x+1\right)+2007\left(x^2+x+1\right)\)

=\(\left(x^2+x+1\right)\left(x^2-x+2008\right)\)

x^4_x+2008(x²+x+1)=x(x-1)(x2+x+1)+2008(x2+x+1)=(x2-x+2008)(x2+x+1)

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

2: \(x^2-x-6=\left(x-3\right)\left(x+2\right)\)

3: \(x^2+7x+12=\left(x+3\right)\left(x+4\right)\)

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

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

3) \(x^2+7x+12=\left(x^2+3x\right)+\left(4x+12\right)=x\left(x+3\right)+4\left(x+3\right)=\left(x+3\right)\left(x+4\right)\)

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

2: \(x^2-x-6=\left(x-3\right)\left(x+2\right)\)

3: \(x^2+7x+12=\left(x+3\right)\left(x+4\right)\)