Factor
\frac{2\left(3-x\right)\left(3x-1\right)}{3}
Evaluate
-2x^{2}+\frac{20x}{3}-2
Graph
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\frac{2\left(-3x^{2}+10x-3\right)}{3}
Factor out \frac{2}{3}.
a+b=10 ab=-3\left(-3\right)=9
Consider -3x^{2}+10x-3. Factor the expression by grouping. First, the expression needs to be rewritten as -3x^{2}+ax+bx-3. To find a and b, set up a system to be solved.
1,9 3,3
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 9.
1+9=10 3+3=6
Calculate the sum for each pair.
a=9 b=1
The solution is the pair that gives sum 10.
\left(-3x^{2}+9x\right)+\left(x-3\right)
Rewrite -3x^{2}+10x-3 as \left(-3x^{2}+9x\right)+\left(x-3\right).
3x\left(-x+3\right)-\left(-x+3\right)
Factor out 3x in the first and -1 in the second group.
\left(-x+3\right)\left(3x-1\right)
Factor out common term -x+3 by using distributive property.
\frac{2\left(-x+3\right)\left(3x-1\right)}{3}
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}