Mister Exam
Factor x^2+2*x+3 squared
The solution
Factorization
[src]
/ ___\ / ___\ \x + 1 + I*\/ 2 /*\x + 1 - I*\/ 2 /
$$\left(x + \left(1 - \sqrt{2} i\right)\right) \left(x + \left(1 + \sqrt{2} i\right)\right)$$
(x + 1 + i*sqrt(2))*(x + 1 - i*sqrt(2))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + 2 x\right) + 3$$
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
$$a = 1$$
$$b = 2$$
$$c = 3$$
Then
$$m = 1$$
$$n = 2$$
So,
$$\left(x + 1\right)^{2} + 2$$
$$\left(x^{2} + 2 x\right) + 3$$
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
$$a = 1$$
$$b = 2$$
$$c = 3$$
Then
$$m = 1$$
$$n = 2$$
So,
$$\left(x + 1\right)^{2} + 2$$