Factor
6x\left(2x-3\right)\left(3x+2\right)
Evaluate
6x\left(2x-3\right)\left(3x+2\right)
Graph
Share
Copied to clipboard
6\left(6x^{3}-5x^{2}-6x\right)
Factor out 6.
x\left(6x^{2}-5x-6\right)
Consider 6x^{3}-5x^{2}-6x. Factor out x.
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 negative, the negative number has greater absolute value than the positive. 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=-9 b=4
The solution is the pair that gives sum -5.
\left(6x^{2}-9x\right)+\left(4x-6\right)
Rewrite 6x^{2}-5x-6 as \left(6x^{2}-9x\right)+\left(4x-6\right).
3x\left(2x-3\right)+2\left(2x-3\right)
Factor out 3x in the first and 2 in the second group.
\left(2x-3\right)\left(3x+2\right)
Factor out common term 2x-3 by using distributive property.
6x\left(2x-3\right)\left(3x+2\right)
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}