Mister Exam
Factor polynomial x^2-10*x+26
The solution
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,
$$\left(x - 5\right)^{2} + 1$$
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)
Combining rational expressions
[src]
26 + x*(-10 + x)
$$x \left(x - 10\right) + 26$$
26 + x*(-10 + x)