1: \(x^2-4x-5=\left(x-5\right)\left(x+1\right)\)
2: \(x^2-x-6=\left(x-3\right)\left(x+2\right)\)
3: \(2x^2-7x+5=\left(x-1\right)\left(2x-5\right)\)
4: \(7x^2+3x-10=\left(x-1\right)\left(7x+10\right)\)
5: \(-5x^2+16x-3\)
\(=-5x^2+15x+x-3\)
\(=-5x\left(x-3\right)+\left(x-3\right)\)
\(=\left(x-3\right)\left(-5x+1\right)\)
6: \(x^2+4x+3=\left(x+1\right)\left(x+3\right)\)
7: \(y^4+4=\left(y^2+2-2y\right)\left(y^2+2+2y\right)\)
8: \(64y^4+x^4\)
\(=64y^4+16y^2x^2+x^4-16y^2x^2\)
\(=\left(x^2+8y^2\right)^2-\left(4xy\right)^2\)
\(=\left(x^2-4xy+8y^2\right)\left(x^2+4xy+8y^2\right)\)
9: \(4y^4+81\)
\(=4y^4+36y^2+81-36y^2\)
\(=\left(2y^2+9\right)^2-\left(6y\right)^2\)
\(=\left(2y^2-6y+9\right)\left(2y^2+6y+9\right)\)
10: \(81x^4+4\)
\(=81x^4+36x^2+4-36x^2\)
\(=\left(9x^2+2\right)^2-36x^2\)
\(=\left(9x^2-6x+2\right)\left(9x^2+6x+2\right)\)
11: Ta có: \(x^7+x^2+1\)
\(=x^7+x^6+x^5-x^6-x^5-x^4+x^4+x^3+x^2-x^3-x^2-x+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^5-x^4+x^2-x+1\right)\)
12: Ta có: \(x^4+4x^2-5\)
\(=x^4+5x^2-x^2-5\)
\(=x^2\left(x^2+5\right)-\left(x^2+5\right)\)
\(=\left(x^2+5\right)\left(x-1\right)\left(x+1\right)\)
13: Ta có: \(x^4+x^2+1\)
\(=\left(x^2+1\right)^2-x^2\)
\(=\left(x^2-x+1\right)\left(x^2+x+1\right)\)
