Mister Exam
Factor polynomial x^2+10*x+26
The solution
Factorization
[src]
(x + 5 + I)*(x + 5 - I)
$$\left(x + \left(5 - i\right)\right) \left(x + \left(5 + i\right)\right)$$
(x + 5 + i)*(x + 5 - i)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + 10 x\right) + 26$$
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
$$a = 1$$
$$b = 10$$
$$c = 26$$
Then
$$m = 5$$
$$n = 1$$
So,
$$\left(x + 5\right)^{2} + 1$$
$$\left(x^{2} + 10 x\right) + 26$$
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
$$a = 1$$
$$b = 10$$
$$c = 26$$
Then
$$m = 5$$
$$n = 1$$
So,
$$\left(x + 5\right)^{2} + 1$$