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x^{2}-3x-4
Multiply and combine like terms.
a+b=-3 ab=1\left(-4\right)=-4
Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-4. To find a and b, set up a system to be solved.
1,-4 2,-2
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 -4.
1-4=-3 2-2=0
Calculate the sum for each pair.
a=-4 b=1
The solution is the pair that gives sum -3.
\left(x^{2}-4x\right)+\left(x-4\right)
Rewrite x^{2}-3x-4 as \left(x^{2}-4x\right)+\left(x-4\right).
x\left(x-4\right)+x-4
Factor out x in x^{2}-4x.
\left(x-4\right)\left(x+1\right)
Factor out common term x-4 by using distributive property.
x^{2}-3x-4
Subtract 2 from -2 to get -4.