\(1,\\ a,\left(x^2+1\right)^2-4x\left(1-x^2\right)\\ =\left(x^2+1\right)^2+4x\left(x^2+1\right)\\ =\left(x^2+1\right)\left(x^2+1+4x\right)\\ b,\left(x^2-8\right)^2+36\\ =x^4-16x^2+64+36\\ =x^4-16x^2+100\\ =x^4-20x^2+100-4x^2\\ =\left(x^2-10\right)^2-4x^2\\ =\left(x^2-10-2x\right)\left(x^2-10+2x\right)\\ c,81x^4+4=81x^4+36x^2+4-36x^2\\ =\left(9x^2+2\right)^2-36x^2\\ =\left(9x^2+2-6x\right)\left(9x^2+2+6x\right)\\ d,x^5+x+1\\ =x^5+x^4+x^3-\left(x^4+x^3+x^2\right)+x^2+x+1\\ =x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+x^2+x+1\\ =\left(x^3-x^2+1\right)\left(x^2+x+1\right)\)
\(2,\\ a,x^3-7x-6\\ =x^3+x^2-x^2-x-6x-6\\ =x^2\left(x+1\right)-x\left(x+1\right)-6\left(x+1\right)\\ =\left(x+1\right)\left(x^2-x-6\right)\\ b,x^3+4x^2-7x-10\\ =x^3-2x^2+6x^2-12x+5x-10\\ =x^2\left(x-2\right)+6x\left(x-2\right)+5\left(x-2\right)\\ =\left(x-2\right)\left(x^2+6x+5\right)\\ =\left(x-2\right)\left(x^2+5x+x+5\right)\\ =\left(x-2\right)\left[x\left(x+5\right)+\left(x+5\right)\right]\\ =\left(x-2\right)\left(x+5\right)\left(x+1\right)\)
Bài 2:
c: \(=x^{10}-x+x^5-x^2+x^2+x+1\)
\(=x\left(x^3-1\right)\left(x^6+x^3+1\right)+x^2\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x\left(x-1\right)\left(x^6+x^3+1\right)+x^2\left(x-1\right)+1\right]\)
