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Expression simplification/ Factorization polynomials/ z^2+5*z-6

Factor polynomial z^2+5*z-6

An expression to simplify:

The solution

You have entered [src] 
 2          
z  + 5*z - 6
$$\left(z^{2} + 5 z\right) - 6$$ 
z^2 + 5*z - 6
General simplification [src] 
      2      
-6 + z  + 5*z
$$z^{2} + 5 z - 6$$ 
-6 + z^2 + 5*z
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(z^{2} + 5 z\right) - 6$$
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
$$a = 1$$
$$b = 5$$
$$c = -6$$
Then
$$m = \frac{5}{2}$$
$$n = - \frac{49}{4}$$
So,
$$\left(z + \frac{5}{2}\right)^{2} - \frac{49}{4}$$
Factorization [src] 
(x + 6)*(x - 1)
$$\left(x - 1\right) \left(x + 6\right)$$ 
(x + 6)*(x - 1)
Rational denominator [src] 
      2      
-6 + z  + 5*z
$$z^{2} + 5 z - 6$$ 
-6 + z^2 + 5*z
Combinatorics [src] 
(-1 + z)*(6 + z)
$$\left(z - 1\right) \left(z + 6\right)$$ 
(-1 + z)*(6 + z)
Common denominator [src] 
      2      
-6 + z  + 5*z
$$z^{2} + 5 z - 6$$ 
-6 + z^2 + 5*z
Assemble expression [src] 
      2      
-6 + z  + 5*z
$$z^{2} + 5 z - 6$$ 
-6 + z^2 + 5*z
Powers [src] 
      2      
-6 + z  + 5*z
$$z^{2} + 5 z - 6$$ 
-6 + z^2 + 5*z
Numerical answer [src] 
-6.0 + z^2 + 5.0*z
-6.0 + z^2 + 5.0*z
Trigonometric part [src] 
      2      
-6 + z  + 5*z
$$z^{2} + 5 z - 6$$ 
-6 + z^2 + 5*z
Combining rational expressions [src] 
-6 + z*(5 + z)
$$z \left(z + 5\right) - 6$$ 
-6 + z*(5 + z)
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