Factor
2x\left(x+1\right)\left(x+5\right)
Evaluate
2x\left(x+1\right)\left(x+5\right)
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2\left(x^{3}+6x^{2}+5x\right)
Factor out 2.
x\left(x^{2}+6x+5\right)
Consider x^{3}+6x^{2}+5x. Factor out x.
a+b=6 ab=1\times 5=5
Consider x^{2}+6x+5. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+5. To find a and b, set up a system to be solved.
a=1 b=5
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.
\left(x^{2}+x\right)+\left(5x+5\right)
Rewrite x^{2}+6x+5 as \left(x^{2}+x\right)+\left(5x+5\right).
x\left(x+1\right)+5\left(x+1\right)
Factor out x in the first and 5 in the second group.
\left(x+1\right)\left(x+5\right)
Factor out common term x+1 by using distributive property.
2x\left(x+1\right)\left(x+5\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}