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$\exponential{(x)}{2} + 4 x - 5 $
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a+b=4 ab=1\left(-5\right)=-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 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(5x-5\right)
Rewrite x^{2}+4x-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.
x^{2}+4x-5=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-4±\sqrt{4^{2}-4\left(-5\right)}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-4±\sqrt{16-4\left(-5\right)}}{2}
Square 4.
x=\frac{-4±\sqrt{16+20}}{2}
Multiply -4 times -5.
x=\frac{-4±\sqrt{36}}{2}
Add 16 to 20.
x=\frac{-4±6}{2}
Take the square root of 36.
x=\frac{2}{2}
Now solve the equation x=\frac{-4±6}{2} when ± is plus. Add -4 to 6.
x=1
Divide 2 by 2.
x=-\frac{10}{2}
Now solve the equation x=\frac{-4±6}{2} when ± is minus. Subtract 6 from -4.
x=-5
Divide -10 by 2.
x^{2}+4x-5=\left(x-1\right)\left(x-\left(-5\right)\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 1 for x_{1} and -5 for x_{2}.
x^{2}+4x-5=\left(x-1\right)\left(x+5\right)
Simplify all the expressions of the form p-\left(-q\right) to p+q.