Factor
-\frac{\left(x-10\right)\left(x+2\right)}{2}
Evaluate
-\frac{\left(x-10\right)\left(x+2\right)}{2}
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\frac{-x^{2}+8x+20}{2}
Factor out \frac{1}{2}.
a+b=8 ab=-20=-20
Consider -x^{2}+8x+20. Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx+20. To find a and b, set up a system to be solved.
-1,20 -2,10 -4,5
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 -20.
-1+20=19 -2+10=8 -4+5=1
Calculate the sum for each pair.
a=10 b=-2
The solution is the pair that gives sum 8.
\left(-x^{2}+10x\right)+\left(-2x+20\right)
Rewrite -x^{2}+8x+20 as \left(-x^{2}+10x\right)+\left(-2x+20\right).
-x\left(x-10\right)-2\left(x-10\right)
Factor out -x in the first and -2 in the second group.
\left(x-10\right)\left(-x-2\right)
Factor out common term x-10 by using distributive property.
\frac{\left(x-10\right)\left(-x-2\right)}{2}
Rewrite the complete factored expression.
Examples
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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
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