Factor
x\left(2x-1\right)\left(x+2\right)
Evaluate
x\left(2x-1\right)\left(x+2\right)
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x\left(2x^{2}+3x-2\right)
Factor out x.
a+b=3 ab=2\left(-2\right)=-4
Consider 2x^{2}+3x-2. Factor the expression by grouping. First, the expression needs to be rewritten as 2x^{2}+ax+bx-2. To find a and b, set up a system to be solved.
-1,4 -2,2
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -4.
-1+4=3 -2+2=0
Calculate the sum for each pair.
a=-1 b=4
The solution is the pair that gives sum 3.
\left(2x^{2}-x\right)+\left(4x-2\right)
Rewrite 2x^{2}+3x-2 as \left(2x^{2}-x\right)+\left(4x-2\right).
x\left(2x-1\right)+2\left(2x-1\right)
Factor out x in the first and 2 in the second group.
\left(2x-1\right)\left(x+2\right)
Factor out common term 2x-1 by using distributive property.
x\left(2x-1\right)\left(x+2\right)
Rewrite the complete factored expression.
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}