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