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\(=\left(2x^4+6x^3\right)-\left(3x^3+9x^2\right)-\left(3x^2-9x\right)+\left(2x+6\right)\)
\(=\left(x+3\right)\left(2x^3-3x^2-3x+2\right)=\left(x+3\right)\left(2x^3-4x^2+x^2-2x-x+2\right)\)
\(=\left(x+3\right)\left(x-2\right)\left(2x^2+x-1\right)=\left(x+3\right)\left(x-2\right)\left(2x^2+2x-x-1\right)\)
\(\left(x+3\right)\left(x-2\right)\left(x+1\right)\left(2x-1\right)\)
\(x^4+3x^2+36\)
\(=\left(x^2\right)^2+2.x^2.6+6^2-9x^2\)
\(=\left(x^2+6\right)^2-\left(3x\right)^2=\left(x^2-3x+6\right)\left(x^2+3x+6\right)\)
\(2x^4-3x^3-7x^2+6x+8\)
\(=2x^4+2x^3-5x^3-5x^2-2x^2-2x+8x+8\)
\(=2x^3\left(x+1\right)-5x^2\left(x+1\right)-2x\left(x+1\right)+8\left(x+1\right)\)
\(=\left(x+1\right)\left(2x^3-5x^2-2x+8\right)\)
\(=\left(x+1\right)\left[2x^2\left(x-2\right)-x\left(x-2\right)-4\left(x-2\right)\right]\)
\(=\left(x+1\right)\left(x-2\right)\left(2x^2-x-4\right)\)
Chúc bạn học tốt.
\(x^4+2x^3+2x^2+2x+1\)
\(=\left(x^4+2x^3+x^2\right)+\left(x^2+2x+1\right)\)
\(=\left(x^2+x\right)^2+\left(x+1\right)^2\)
\(=x^2\left(x+1\right)^2+\left(x+1\right)^2\)
\(=\left(x+1\right)^2\left(x^2+1\right)\)