Phan tich 3x2-x-4 thanh phan tu
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x4+x2+1
=(x2)2+2x2+1-2x2+x2
=(x2+1)2-2x2+x2
= (x² + 1)² − x²
= (x² + x+ 1 )(x² − x+ 1 )
\(x^4+x^2+1\)
\(=\left[\left(x^2\right)^2+2.x^2.\frac{1}{2}+\left(\frac{1}{2}\right)^2\right]-\left(\frac{1}{2}\right)^2+1\)
\(=\left(x^2+\frac{1}{2}\right)^2-\frac{1}{4}+\frac{4}{4}\)
\(=\left(x^2+\frac{1}{2}\right)^2+\frac{3}{4}\)
\(=\left(x^2\right)^2-\left(y^3\right)^2=\left(x^2-y^3\right)\left(x^2+y^3\right)\)
\(x^2-3x+4\)
\(=x^2+x-4x+4\)
\(=\left(x^2+x\right)-\left(4x+4\right)\)
\(=x\left(x+1\right)-4\left(x+1\right)\)
\(=\left(x-4\right)\left(x+1\right)\).
ta có : x^8 +x^4 +1= (x^8 -x^5) +(x^5-x^2) +(x^4 -x) +(x^2 +x 1)=x^5.(x^3 -1) +x^2(x^3-1) +x(x^3-1) +(x^2 +x+1)=x^5.(x-1)(x^2 +x+1) +x^2(x-1)(x^2 +x+1) +x(x-1)(x^2 +x+1) +(x^2 +x+10=(x^2 +x+1)(x^6- x^5 +x^3 -x +1)
\(3x^2-x-4\)
\(=3x^2+3x-4x-4\)
\(=3x\left(x+1\right)-4\left(x+1\right)\)
\(=\left(3x-4\right)\left(x+1\right)\)