Mister Exam
Factor -y^2+2*y+5 squared
The solution
Factorization
[src]
/ ___\ / ___\ \x + -1 + \/ 6 /*\x + -1 - \/ 6 /
$$\left(x + \left(-1 + \sqrt{6}\right)\right) \left(x + \left(- \sqrt{6} - 1\right)\right)$$
(x - 1 + sqrt(6))*(x - 1 - sqrt(6))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{2} + 2 y\right) + 5$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = 2$$
$$c = 5$$
Then
$$m = -1$$
$$n = 6$$
So,
$$6 - \left(y - 1\right)^{2}$$
$$\left(- y^{2} + 2 y\right) + 5$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = 2$$
$$c = 5$$
Then
$$m = -1$$
$$n = 6$$
So,
$$6 - \left(y - 1\right)^{2}$$