a) Ta có:
\(2x^3-5x^2+8x-3\)
\(=2x^3-x^2-4x^2+2x+6x-3\)
\(=x^2\left(2x-1\right)-2x\left(2x-1\right)+3\left(2x-1\right)\)
\(=\left(2x-1\right)\left(x^2-2x+3\right)\)
\(=2\left(x-\dfrac{1}{2}\right)\left(x^2-2x+3\right)\)
b) Ta có:
\(\left(x^2+x\right)^2+4x^2+4x-12\)
\(=x^4+2x^3+x^2+4x^2+4x-12\)
\(=x^4+2x^3+5x^2+4x-12\)
\(=x^4+2x^3+5x^2+10x-6x-12\)
\(=x^3\left(x+2\right)+5x\left(x+2\right)-6\left(x+2\right)\)
\(=\left(x+2\right)\left(x^3+5x-6\right)\)
\(=\left(x+2\right)\left(x^3-x^2+x^2-x+6x-6\right)\)
\(=\left(x+2\right)\left[x^2\left(x-1\right)+x\left(x-1\right)+6\left(x-1\right)\right]\)
\(=\left(x+2\right)\left(x-1\right)\left(x^2+x+6\right)\)
