Bài 3: Phân tích đa thức thành nhân tử
a) Ta có: \(x^2-4x+3\)
\(=x^2-x-3x+3\)
\(=x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(x-1\right)\left(x-3\right)\)
b) Ta có: \(x^2+4x-12\)
\(=x^2+6x-2x-12\)
\(=x\left(x+6\right)-2\left(x+6\right)\)
\(=\left(x+6\right)\left(x-2\right)\)
c) Ta có: \(2x^2-3x-2\)
\(=2x^2-4x+x-2\)
\(=2x\left(x-2\right)+\left(x-2\right)\)
\(=\left(x-2\right)\left(2x+1\right)\)
d) Ta có: \(2x^3+x-2x^2-1\)
\(=2x^2\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(2x^2+1\right)\)
e) Ta có: \(x^4+2x^2-8\)
\(=x^4+4x^2-2x^2-8\)
\(=x^2\left(x^2+4\right)-2\left(x^2+4\right)\)
\(=\left(x^2+4\right)\cdot\left(x^2-2\right)\)
f) Ta có: \(x^2-2xy-3y^2\)
\(=x^2-3xy+xy-3y^2\)
\(=x\left(x-3y\right)+y\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+y\right)\)
