Mister Exam
Factor polynomial x^2-x-12
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - x\right) - 12$$
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
$$a = 1$$
$$b = -1$$
$$c = -12$$
Then
$$m = - \frac{1}{2}$$
$$n = - \frac{49}{4}$$
So,
$$\left(x - \frac{1}{2}\right)^{2} - \frac{49}{4}$$
$$\left(x^{2} - x\right) - 12$$
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
$$a = 1$$
$$b = -1$$
$$c = -12$$
Then
$$m = - \frac{1}{2}$$
$$n = - \frac{49}{4}$$
So,
$$\left(x - \frac{1}{2}\right)^{2} - \frac{49}{4}$$
Combining rational expressions
[src]
-12 + x*(-1 + x)
$$x \left(x - 1\right) - 12$$
-12 + x*(-1 + x)