Factor
x\left(x-1\right)\left(2x-3\right)
Evaluate
x\left(x-1\right)\left(2x-3\right)
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x\left(2x^{2}-5x+3\right)
Factor out x.
a+b=-5 ab=2\times 3=6
Consider 2x^{2}-5x+3. Factor the expression by grouping. First, the expression needs to be rewritten as 2x^{2}+ax+bx+3. To find a and b, set up a system to be solved.
-1,-6 -2,-3
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 6.
-1-6=-7 -2-3=-5
Calculate the sum for each pair.
a=-3 b=-2
The solution is the pair that gives sum -5.
\left(2x^{2}-3x\right)+\left(-2x+3\right)
Rewrite 2x^{2}-5x+3 as \left(2x^{2}-3x\right)+\left(-2x+3\right).
x\left(2x-3\right)-\left(2x-3\right)
Factor out x in the first and -1 in the second group.
\left(2x-3\right)\left(x-1\right)
Factor out common term 2x-3 by using distributive property.
x\left(2x-3\right)\left(x-1\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}