Factor
\frac{\left(3x-2\right)\left(2x+3\right)}{3}
Evaluate
2x^{2}+\frac{5x}{3}-2
Graph
Share
Copied to clipboard
\frac{6x^{2}+5x-6}{3}
Factor out \frac{1}{3}.
a+b=5 ab=6\left(-6\right)=-36
Consider 6x^{2}+5x-6. Factor the expression by grouping. First, the expression needs to be rewritten as 6x^{2}+ax+bx-6. To find a and b, set up a system to be solved.
-1,36 -2,18 -3,12 -4,9 -6,6
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 -36.
-1+36=35 -2+18=16 -3+12=9 -4+9=5 -6+6=0
Calculate the sum for each pair.
a=-4 b=9
The solution is the pair that gives sum 5.
\left(6x^{2}-4x\right)+\left(9x-6\right)
Rewrite 6x^{2}+5x-6 as \left(6x^{2}-4x\right)+\left(9x-6\right).
2x\left(3x-2\right)+3\left(3x-2\right)
Factor out 2x in the first and 3 in the second group.
\left(3x-2\right)\left(2x+3\right)
Factor out common term 3x-2 by using distributive property.
\frac{\left(3x-2\right)\left(2x+3\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}