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Expression simplification/ Factorization polynomials/ z^2+z-4

Factor polynomial z^2+z-4

An expression to simplify:

The solution

You have entered [src] 
 2        
z  + z - 4
$$\left(z^{2} + z\right) - 4$$ 
z^2 + z - 4
Factorization [src] 
/          ____\ /          ____\
|    1   \/ 17 | |    1   \/ 17 |
|x + - - ------|*|x + - + ------|
\    2     2   / \    2     2   /
$$\left(x + \left(\frac{1}{2} - \frac{\sqrt{17}}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{17}}{2}\right)\right)$$ 
(x + 1/2 - sqrt(17)/2)*(x + 1/2 + sqrt(17)/2)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(z^{2} + z\right) - 4$$
To do this, let's use the formula
$$a z^{2} + b z + c = a \left(m + z\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 1$$
$$c = -4$$
Then
$$m = \frac{1}{2}$$
$$n = - \frac{17}{4}$$
So,
$$\left(z + \frac{1}{2}\right)^{2} - \frac{17}{4}$$
General simplification [src] 
          2
-4 + z + z
$$z^{2} + z - 4$$ 
-4 + z + z^2
Combinatorics [src] 
          2
-4 + z + z
$$z^{2} + z - 4$$ 
-4 + z + z^2
Powers [src] 
          2
-4 + z + z
$$z^{2} + z - 4$$ 
-4 + z + z^2
Numerical answer [src] 
-4.0 + z + z^2
-4.0 + z + z^2
Trigonometric part [src] 
          2
-4 + z + z
$$z^{2} + z - 4$$ 
-4 + z + z^2
Common denominator [src] 
          2
-4 + z + z
$$z^{2} + z - 4$$ 
-4 + z + z^2
Assemble expression [src] 
          2
-4 + z + z
$$z^{2} + z - 4$$ 
-4 + z + z^2
Rational denominator [src] 
          2
-4 + z + z
$$z^{2} + z - 4$$ 
-4 + z + z^2
Combining rational expressions [src] 
-4 + z*(1 + z)
$$z \left(z + 1\right) - 4$$ 
-4 + z*(1 + z)
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