Mister Exam
Factor polynomial x^2-7*x+10
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - 7 x\right) + 10$$
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
$$a = 1$$
$$b = -7$$
$$c = 10$$
Then
$$m = - \frac{7}{2}$$
$$n = - \frac{9}{4}$$
So,
$$\left(x - \frac{7}{2}\right)^{2} - \frac{9}{4}$$
$$\left(x^{2} - 7 x\right) + 10$$
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
$$a = 1$$
$$b = -7$$
$$c = 10$$
Then
$$m = - \frac{7}{2}$$
$$n = - \frac{9}{4}$$
So,
$$\left(x - \frac{7}{2}\right)^{2} - \frac{9}{4}$$