Mister Exam
Factor x^2*(-2)+5*x-2 squared
The solution
You have entered
[src]
2 x *(-2) + 5*x - 2
$$\left(\left(-2\right) x^{2} + 5 x\right) - 2$$
x^2*(-2) + 5*x - 2
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(\left(-2\right) x^{2} + 5 x\right) - 2$$
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
$$a = -2$$
$$b = 5$$
$$c = -2$$
Then
$$m = - \frac{5}{4}$$
$$n = \frac{9}{8}$$
So,
$$\frac{9}{8} - 2 \left(x - \frac{5}{4}\right)^{2}$$
$$\left(\left(-2\right) x^{2} + 5 x\right) - 2$$
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
$$a = -2$$
$$b = 5$$
$$c = -2$$
Then
$$m = - \frac{5}{4}$$
$$n = \frac{9}{8}$$
So,
$$\frac{9}{8} - 2 \left(x - \frac{5}{4}\right)^{2}$$
Factorization
[src]
(x - 1/2)*(x - 2)
$$\left(x - 2\right) \left(x - \frac{1}{2}\right)$$
(x - 1/2)*(x - 2)
Combining rational expressions
[src]
-2 + x*(5 - 2*x)
$$x \left(5 - 2 x\right) - 2$$
-2 + x*(5 - 2*x)
Combinatorics
[src]
-(-1 + 2*x)*(-2 + x)
$$- \left(x - 2\right) \left(2 x - 1\right)$$
-(-1 + 2*x)*(-2 + x)