Evaluate
\left(3x-2\right)\left(2x+1\right)
Factor
\left(3x-2\right)\left(2x+1\right)
Graph
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3x-2+5x^{2}-4x+x^{2}
Add -4 and 2 to get -2.
-x-2+5x^{2}+x^{2}
Combine 3x and -4x to get -x.
-x-2+6x^{2}
Combine 5x^{2} and x^{2} to get 6x^{2}.
6x^{2}-x-2
Multiply and combine like terms.
a+b=-1 ab=6\left(-2\right)=-12
Factor the expression by grouping. First, the expression needs to be rewritten as 6x^{2}+ax+bx-2. To find a and b, set up a system to be solved.
1,-12 2,-6 3,-4
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -12.
1-12=-11 2-6=-4 3-4=-1
Calculate the sum for each pair.
a=-4 b=3
The solution is the pair that gives sum -1.
\left(6x^{2}-4x\right)+\left(3x-2\right)
Rewrite 6x^{2}-x-2 as \left(6x^{2}-4x\right)+\left(3x-2\right).
2x\left(3x-2\right)+3x-2
Factor out 2x in 6x^{2}-4x.
\left(3x-2\right)\left(2x+1\right)
Factor out common term 3x-2 by using distributive property.
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}