Mister Exam
Factor polynomial x^2-24*x+144
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - 24 x\right) + 144$$
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
$$a = 1$$
$$b = -24$$
$$c = 144$$
Then
$$m = -12$$
$$n = 0$$
So,
$$\left(x - 12\right)^{2}$$
$$\left(x^{2} - 24 x\right) + 144$$
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
$$a = 1$$
$$b = -24$$
$$c = 144$$
Then
$$m = -12$$
$$n = 0$$
So,
$$\left(x - 12\right)^{2}$$
Combining rational expressions
[src]
144 + x*(-24 + x)
$$x \left(x - 24\right) + 144$$
144 + x*(-24 + x)