Mister Exam

Other calculators

Expression simplification/ Factorization polynomials/ x^2+x-2

Factor polynomial x^2+x-2

An expression to simplify:

The solution

You have entered [src] 
 2        
x  + x - 2
(x2+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
(x2+x)−2\left(x^{2} + x\right) - 2
To do this, let's use the formula
ax2+bx+c=a(m+x)2+na x^{2} + b x + c = a \left(m + x\right)^{2} + n
where
m=b2am = \frac{b}{2 a}
n=4ac−b24an = \frac{4 a c - b^{2}}{4 a}
In this case
a=1a = 1
b=1b = 1
c=−2c = -2
Then
m=12m = \frac{1}{2}
n=−94n = - \frac{9}{4}
So,
(x+12)2−94\left(x + \frac{1}{2}\right)^{2} - \frac{9}{4}
General simplification [src] 
          2
-2 + x + x
x2+x−2x^{2} + x - 2 
-2 + x + x^2
Factorization [src] 
(x + 2)*(x - 1)
(x−1)(x+2)\left(x - 1\right) \left(x + 2\right) 
(x + 2)*(x - 1)
Rational denominator [src] 
          2
-2 + x + x
x2+x−2x^{2} + x - 2 
-2 + x + x^2
Common denominator [src] 
          2
-2 + x + x
x2+x−2x^{2} + x - 2 
-2 + x + x^2
Assemble expression [src] 
          2
-2 + x + x
x2+x−2x^{2} + x - 2 
-2 + x + x^2
Combining rational expressions [src] 
-2 + x*(1 + x)
x(x+1)−2x \left(x + 1\right) - 2 
-2 + x*(1 + x)
Combinatorics [src] 
(-1 + x)*(2 + x)
(x−1)(x+2)\left(x - 1\right) \left(x + 2\right) 
(-1 + x)*(2 + x)
Powers [src] 
          2
-2 + x + x
x2+x−2x^{2} + x - 2 
-2 + x + x^2
Trigonometric part [src] 
          2
-2 + x + x
x2+x−2x^{2} + x - 2 
-2 + x + x^2
Numerical answer [src] 
-2.0 + x + x^2
-2.0 + x + x^2
    © Mister Exam – Calculator