Question

2x cube + x square - 4x

Factorize

Answer 1

$2x^{3} +x^{2} -4x\\=2x (x^{2} +\frac{x}{2}-2)\\=2x (x^{2} +2.\frac{x}{2}.\frac{1}{2}+\frac{1}{4} -2-\frac{1}{4} )\\=2x ((x+\frac{1}{2})^{2} -\frac{2.4+1}{4} )\\=2x((x+\frac{1}{2})^{2} -(\frac{3}{2})^2)\\=2x(x+\frac{1}{2}+\frac{3}{2})(x+\frac{1}{2}-\frac{3}{2})\\=2x(x+\frac{4}{2})(x-\frac{2}{2}))\\=2x(x+2)(x-1)$

This is the correct factorization answer.