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Factor polynomial y^2-4*y-42

An expression to simplify:

The solution

You have entered [src]
 2           
y  - 4*y - 42
$$\left(y^{2} - 4 y\right) - 42$$
y^2 - 4*y - 42
Factorization [src]
/           ____\ /           ____\
\x + -2 + \/ 46 /*\x + -2 - \/ 46 /
$$\left(x + \left(-2 + \sqrt{46}\right)\right) \left(x + \left(- \sqrt{46} - 2\right)\right)$$
(x - 2 + sqrt(46))*(x - 2 - sqrt(46))
General simplification [src]
       2      
-42 + y  - 4*y
$$y^{2} - 4 y - 42$$
-42 + y^2 - 4*y
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{2} - 4 y\right) - 42$$
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
$$a = 1$$
$$b = -4$$
$$c = -42$$
Then
$$m = -2$$
$$n = -46$$
So,
$$\left(y - 2\right)^{2} - 46$$
Numerical answer [src]
-42.0 + y^2 - 4.0*y
-42.0 + y^2 - 4.0*y
Assemble expression [src]
       2      
-42 + y  - 4*y
$$y^{2} - 4 y - 42$$
-42 + y^2 - 4*y
Combining rational expressions [src]
-42 + y*(-4 + y)
$$y \left(y - 4\right) - 42$$
-42 + y*(-4 + y)
Trigonometric part [src]
       2      
-42 + y  - 4*y
$$y^{2} - 4 y - 42$$
-42 + y^2 - 4*y
Powers [src]
       2      
-42 + y  - 4*y
$$y^{2} - 4 y - 42$$
-42 + y^2 - 4*y
Rational denominator [src]
       2      
-42 + y  - 4*y
$$y^{2} - 4 y - 42$$
-42 + y^2 - 4*y
Common denominator [src]
       2      
-42 + y  - 4*y
$$y^{2} - 4 y - 42$$
-42 + y^2 - 4*y
Combinatorics [src]
       2      
-42 + y  - 4*y
$$y^{2} - 4 y - 42$$
-42 + y^2 - 4*y