Mister Exam

Other calculators

Expression simplification/ Factorization polynomials/ y^2+y-6

Factor polynomial y^2+y-6

An expression to simplify:

The solution

You have entered [src] 
 2        
y  + y - 6
$$\left(y^{2} + y\right) - 6$$ 
y^2 + y - 6
Factorization [src] 
(x + 3)*(x - 2)
$$\left(x - 2\right) \left(x + 3\right)$$ 
(x + 3)*(x - 2)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{2} + y\right) - 6$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 1$$
$$c = -6$$
Then
$$m = \frac{1}{2}$$
$$n = - \frac{25}{4}$$
So,
$$\left(y + \frac{1}{2}\right)^{2} - \frac{25}{4}$$
General simplification [src] 
          2
-6 + y + y
$$y^{2} + y - 6$$ 
-6 + y + y^2
Rational denominator [src] 
          2
-6 + y + y
$$y^{2} + y - 6$$ 
-6 + y + y^2
Trigonometric part [src] 
          2
-6 + y + y
$$y^{2} + y - 6$$ 
-6 + y + y^2
Assemble expression [src] 
          2
-6 + y + y
$$y^{2} + y - 6$$ 
-6 + y + y^2
Numerical answer [src] 
-6.0 + y + y^2
-6.0 + y + y^2
Powers [src] 
          2
-6 + y + y
$$y^{2} + y - 6$$ 
-6 + y + y^2
Common denominator [src] 
          2
-6 + y + y
$$y^{2} + y - 6$$ 
-6 + y + y^2
Combinatorics [src] 
(-2 + y)*(3 + y)
$$\left(y - 2\right) \left(y + 3\right)$$ 
(-2 + y)*(3 + y)
Combining rational expressions [src] 
-6 + y*(1 + y)
$$y \left(y + 1\right) - 6$$ 
-6 + y*(1 + y)
    © Mister Exam – Calculator