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Expression simplification/ Factorization polynomials/ x^2-5*x+4

Factor polynomial x^2-5*x+4

An expression to simplify:

The solution

You have entered [src] 
 2          
x  - 5*x + 4
$$\left(x^{2} - 5 x\right) + 4$$ 
x^2 - 5*x + 4
General simplification [src] 
     2      
4 + x  - 5*x
$$x^{2} - 5 x + 4$$ 
4 + x^2 - 5*x
Factorization [src] 
(x - 1)*(x - 4)
$$\left(x - 4\right) \left(x - 1\right)$$ 
(x - 1)*(x - 4)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - 5 x\right) + 4$$
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
$$a = 1$$
$$b = -5$$
$$c = 4$$
Then
$$m = - \frac{5}{2}$$
$$n = - \frac{9}{4}$$
So,
$$\left(x - \frac{5}{2}\right)^{2} - \frac{9}{4}$$
Trigonometric part [src] 
     2      
4 + x  - 5*x
$$x^{2} - 5 x + 4$$ 
4 + x^2 - 5*x
Combinatorics [src] 
(-1 + x)*(-4 + x)
$$\left(x - 4\right) \left(x - 1\right)$$ 
(-1 + x)*(-4 + x)
Powers [src] 
     2      
4 + x  - 5*x
$$x^{2} - 5 x + 4$$ 
4 + x^2 - 5*x
Common denominator [src] 
     2      
4 + x  - 5*x
$$x^{2} - 5 x + 4$$ 
4 + x^2 - 5*x
Combining rational expressions [src] 
4 + x*(-5 + x)
$$x \left(x - 5\right) + 4$$ 
4 + x*(-5 + x)
Assemble expression [src] 
     2      
4 + x  - 5*x
$$x^{2} - 5 x + 4$$ 
4 + x^2 - 5*x
Numerical answer [src] 
4.0 + x^2 - 5.0*x
4.0 + x^2 - 5.0*x
Rational denominator [src] 
     2      
4 + x  - 5*x
$$x^{2} - 5 x + 4$$ 
4 + x^2 - 5*x
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