Mister Exam
Factor 2*x^2+3*x-5 squared
The solution
Factorization
[src]
(x + 5/2)*(x - 1)
$$\left(x - 1\right) \left(x + \frac{5}{2}\right)$$
(x + 5/2)*(x - 1)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(2 x^{2} + 3 x\right) - 5$$
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
$$a = 2$$
$$b = 3$$
$$c = -5$$
Then
$$m = \frac{3}{4}$$
$$n = - \frac{49}{8}$$
So,
$$2 \left(x + \frac{3}{4}\right)^{2} - \frac{49}{8}$$
$$\left(2 x^{2} + 3 x\right) - 5$$
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
$$a = 2$$
$$b = 3$$
$$c = -5$$
Then
$$m = \frac{3}{4}$$
$$n = - \frac{49}{8}$$
So,
$$2 \left(x + \frac{3}{4}\right)^{2} - \frac{49}{8}$$
Combinatorics
[src]
(-1 + x)*(5 + 2*x)
$$\left(x - 1\right) \left(2 x + 5\right)$$
(-1 + x)*(5 + 2*x)
Combining rational expressions
[src]
-5 + x*(3 + 2*x)
$$x \left(2 x + 3\right) - 5$$
-5 + x*(3 + 2*x)