Mister Exam
Factor x^2-2*x+12 squared
The solution
Factorization
[src]
/ ____\ / ____\ \x + -1 + I*\/ 11 /*\x + -1 - I*\/ 11 /
$$\left(x + \left(-1 - \sqrt{11} i\right)\right) \left(x + \left(-1 + \sqrt{11} i\right)\right)$$
(x - 1 + i*sqrt(11))*(x - 1 - i*sqrt(11))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - 2 x\right) + 12$$
To do this, let's use the formula
$$a x^{2} + b x + c = a \left(m + x\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = -2$$
$$c = 12$$
Then
$$m = -1$$
$$n = 11$$
So,
$$\left(x - 1\right)^{2} + 11$$
$$\left(x^{2} - 2 x\right) + 12$$
To do this, let's use the formula
$$a x^{2} + b x + c = a \left(m + x\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = -2$$
$$c = 12$$
Then
$$m = -1$$
$$n = 11$$
So,
$$\left(x - 1\right)^{2} + 11$$