Factor
\left(x-1\right)\left(3x+1\right)
Evaluate
\left(x-1\right)\left(3x+1\right)
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3x^{2}-2x-1
Multiply and combine like terms.
a+b=-2 ab=3\left(-1\right)=-3
Factor the expression by grouping. First, the expression needs to be rewritten as 3x^{2}+ax+bx-1. To find a and b, set up a system to be solved.
a=-3 b=1
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. The only such pair is the system solution.
\left(3x^{2}-3x\right)+\left(x-1\right)
Rewrite 3x^{2}-2x-1 as \left(3x^{2}-3x\right)+\left(x-1\right).
3x\left(x-1\right)+x-1
Factor out 3x in 3x^{2}-3x.
\left(x-1\right)\left(3x+1\right)
Factor out common term x-1 by using distributive property.
3x^{2}-2x-1
Subtract 2 from 1 to get -1.
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}