Factor
\left(x-1\right)\left(x+7\right)
Evaluate
\left(x-1\right)\left(x+7\right)
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x^{2}+6x-7
Multiply and combine like terms.
a+b=6 ab=1\left(-7\right)=-7
Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-7. To find a and b, set up a system to be solved.
a=-1 b=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. The only such pair is the system solution.
\left(x^{2}-x\right)+\left(7x-7\right)
Rewrite x^{2}+6x-7 as \left(x^{2}-x\right)+\left(7x-7\right).
x\left(x-1\right)+7\left(x-1\right)
Factor out x in the first and 7 in the second group.
\left(x-1\right)\left(x+7\right)
Factor out common term x-1 by using distributive property.
x^{2}+6x-7
Combine -x and 7x to get 6x.
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