Mister Exam
Factor polynomial z^2-6*z+5
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(z^{2} - 6 z\right) + 5$$
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
$$a = 1$$
$$b = -6$$
$$c = 5$$
Then
$$m = -3$$
$$n = -4$$
So,
$$\left(z - 3\right)^{2} - 4$$
$$\left(z^{2} - 6 z\right) + 5$$
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
$$a = 1$$
$$b = -6$$
$$c = 5$$
Then
$$m = -3$$
$$n = -4$$
So,
$$\left(z - 3\right)^{2} - 4$$