Mister Exam

# Factor polynomial x^2+x-2

An expression to simplify:

### The solution

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 2
x  + x - 2
$$\left(x^{2} + x\right) - 2$$
x^2 + x - 2
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + x\right) - 2$$
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
$$a = 1$$
$$b = 1$$
$$c = -2$$
Then
$$m = \frac{1}{2}$$
$$n = - \frac{9}{4}$$
So,
$$\left(x + \frac{1}{2}\right)^{2} - \frac{9}{4}$$
General simplification [src]
          2
-2 + x + x 
$$x^{2} + x - 2$$
-2 + x + x^2
Factorization [src]
(x + 2)*(x - 1)
$$\left(x - 1\right) \left(x + 2\right)$$
(x + 2)*(x - 1)
Rational denominator [src]
          2
-2 + x + x 
$$x^{2} + x - 2$$
-2 + x + x^2
Common denominator [src]
          2
-2 + x + x 
$$x^{2} + x - 2$$
-2 + x + x^2
Assemble expression [src]
          2
-2 + x + x 
$$x^{2} + x - 2$$
-2 + x + x^2
Combining rational expressions [src]
-2 + x*(1 + x)
$$x \left(x + 1\right) - 2$$
-2 + x*(1 + x)
Combinatorics [src]
(-1 + x)*(2 + x)
$$\left(x - 1\right) \left(x + 2\right)$$
(-1 + x)*(2 + x)
Powers [src]
          2
-2 + x + x 
$$x^{2} + x - 2$$
-2 + x + x^2
Trigonometric part [src]
          2
-2 + x + x 
$$x^{2} + x - 2$$
-2 + x + x^2
-2.0 + x + x^2
-2.0 + x + x^2