Factor
\left(x-2\right)\left(x+7\right)
Evaluate
\left(x-2\right)\left(x+7\right)
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x^{2}+5x-14
Multiply and combine like terms.
a+b=5 ab=1\left(-14\right)=-14
Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-14. To find a and b, set up a system to be solved.
-1,14 -2,7
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 -14.
-1+14=13 -2+7=5
Calculate the sum for each pair.
a=-2 b=7
The solution is the pair that gives sum 5.
\left(x^{2}-2x\right)+\left(7x-14\right)
Rewrite x^{2}+5x-14 as \left(x^{2}-2x\right)+\left(7x-14\right).
x\left(x-2\right)+7\left(x-2\right)
Factor out x in the first and 7 in the second group.
\left(x-2\right)\left(x+7\right)
Factor out common term x-2 by using distributive property.
x^{2}+5x-14
Combine -2x and 7x to get 5x.
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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