Factor
2x\left(x+1\right)\left(-2x^{2}+3x-2\right)
Evaluate
2x\left(x+1\right)\left(-2x^{2}+3x-2\right)
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2\left(x^{3}-2x+x^{2}-2x^{4}\right)
Factor out 2.
x\left(x^{2}-2+x-2x^{3}\right)
Consider x^{3}-2x+x^{2}-2x^{4}. Factor out x.
\left(x+1\right)\left(-2x^{2}+3x-2\right)
Consider x^{2}-2+x-2x^{3}. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -2 and q divides the leading coefficient -2. One such root is -1. Factor the polynomial by dividing it by x+1.
2x\left(x+1\right)\left(-2x^{2}+3x-2\right)
Rewrite the complete factored expression. Polynomial -2x^{2}+3x-2 is not factored since it does not have any rational roots.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}