Factor
\frac{2\left(1-x\right)\left(3x+2\right)}{7}
Evaluate
\frac{2\left(2+x-3x^{2}\right)}{7}
Graph
Share
Copied to clipboard
\frac{2\left(2+x-3x^{2}\right)}{7}
Factor out \frac{2}{7}.
-3x^{2}+x+2
Consider 2+x-3x^{2}. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
a+b=1 ab=-3\times 2=-6
Factor the expression by grouping. First, the expression needs to be rewritten as -3x^{2}+ax+bx+2. To find a and b, set up a system to be solved.
-1,6 -2,3
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 -6.
-1+6=5 -2+3=1
Calculate the sum for each pair.
a=3 b=-2
The solution is the pair that gives sum 1.
\left(-3x^{2}+3x\right)+\left(-2x+2\right)
Rewrite -3x^{2}+x+2 as \left(-3x^{2}+3x\right)+\left(-2x+2\right).
3x\left(-x+1\right)+2\left(-x+1\right)
Factor out 3x in the first and 2 in the second group.
\left(-x+1\right)\left(3x+2\right)
Factor out common term -x+1 by using distributive property.
\frac{2\left(-x+1\right)\left(3x+2\right)}{7}
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}