Mister Exam
Factor x^2-9*x-10 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - 9 x\right) - 10$$
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
$$a = 1$$
$$b = -9$$
$$c = -10$$
Then
$$m = - \frac{9}{2}$$
$$n = - \frac{121}{4}$$
So,
$$\left(x - \frac{9}{2}\right)^{2} - \frac{121}{4}$$
$$\left(x^{2} - 9 x\right) - 10$$
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
$$a = 1$$
$$b = -9$$
$$c = -10$$
Then
$$m = - \frac{9}{2}$$
$$n = - \frac{121}{4}$$
So,
$$\left(x - \frac{9}{2}\right)^{2} - \frac{121}{4}$$
Combining rational expressions
[src]
-10 + x*(-9 + x)
$$x \left(x - 9\right) - 10$$
-10 + x*(-9 + x)