Mister Exam

Factor polynomial z^2-20*z+104

An expression to simplify:

The solution

You have entered [src]
 2             
z  - 20*z + 104
$$\left(z^{2} - 20 z\right) + 104$$
z^2 - 20*z + 104
General simplification [src]
       2       
104 + z  - 20*z
$$z^{2} - 20 z + 104$$
104 + z^2 - 20*z
Factorization [src]
(x + -10 + 2*I)*(x + -10 - 2*I)
$$\left(x + \left(-10 - 2 i\right)\right) \left(x + \left(-10 + 2 i\right)\right)$$
(x - 10 + 2*i)*(x - 10 - 2*i)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(z^{2} - 20 z\right) + 104$$
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
$$a = 1$$
$$b = -20$$
$$c = 104$$
Then
$$m = -10$$
$$n = 4$$
So,
$$\left(z - 10\right)^{2} + 4$$
Combinatorics [src]
       2       
104 + z  - 20*z
$$z^{2} - 20 z + 104$$
104 + z^2 - 20*z
Powers [src]
       2       
104 + z  - 20*z
$$z^{2} - 20 z + 104$$
104 + z^2 - 20*z
Trigonometric part [src]
       2       
104 + z  - 20*z
$$z^{2} - 20 z + 104$$
104 + z^2 - 20*z
Numerical answer [src]
104.0 + z^2 - 20.0*z
104.0 + z^2 - 20.0*z
Rational denominator [src]
       2       
104 + z  - 20*z
$$z^{2} - 20 z + 104$$
104 + z^2 - 20*z
Common denominator [src]
       2       
104 + z  - 20*z
$$z^{2} - 20 z + 104$$
104 + z^2 - 20*z
Assemble expression [src]
       2       
104 + z  - 20*z
$$z^{2} - 20 z + 104$$
104 + z^2 - 20*z
Combining rational expressions [src]
104 + z*(-20 + z)
$$z \left(z - 20\right) + 104$$
104 + z*(-20 + z)