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\(x^8+x+1\)
\(=\left(x^8-x^5\right)+\left(x^5-x^2\right)+\left(x^2+x+1\right)\)
\(x^5\left(x^3-1\right)+x^2\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(=x^5\left(x-1\right)\left(x^2+x+1\right)+x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^6-x^5\right)\left(x^2+x+1\right)+\left(x^3-x^2\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
\(x^8+3x^3+1\)
\(=x^8-x^4+4x^4+4\)
\(=\left(x^4-1\right)\cdot\left(x^4+1\right)+4\cdot\left(x^4+1\right)\)
\(=\left(x^4+1\right)\cdot\left(x^4-1+4\right)\)
\(=\left(x^4+1\right)\cdot\left(x^4+3\right)\)
=x11-x2+x2+x+1
=x2(x9-1)+(x2+x+1)
=x2[(x3)3-13)+(x2+x+1)
=x2(x3-1)(x6+x3+1)+(x2+x+1)
=x2(x6+x3+1)(x-1)(x2+x+1)+(x2+x+1)
Đặt nhân tử chung là x2+x+1 rồi phá hết ngoặc là xong
\(=x^2+2x\cdot\frac{1}{2}+\frac{1}{4}-\left(\frac{\sqrt{23}}{2}i\right)^2\)
\(=\left(x+\frac{1}{2}\right)^2\)\(-\left(\frac{\sqrt{23}}{2}i\right)^2\)
\(\left(x+\frac{1}{2}-\frac{\sqrt{23}}{2}i\right)\left(x+\frac{1}{2}+\frac{\sqrt[]{23}}{2}i\right)\)
cá này là bình phương thếu.k thể phân tích thành nhân tử dc nữa
\(x^3-x^2-14x+24\)
\(=x^3+4x^2-5x^2-20x+6x+24\)
\(=\left(x^3+4x^2\right)-\left(5x^2+20x\right)+\left(6x+24\right)\)
\(=x^2\left(x+4\right)-5x\left(x+4\right)+6\left(x+4\right)\)
\(=\left(x^2-5x+6\right)\left(x+4\right)\)
\(=\left(x^2-2x-3x+6\right)\left(x+4\right)\)
\(=\left[x\left(x-2\right)-3\left(x-2\right)\right]\left(x+4\right)\)
\(=\left(x-2\right)\left(x-3\right)\left(x+4\right)\)
\(x^8+x+1\)
\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^6-x^5+x^3-x^2+1\right)\left(x^2+x+1\right)\)