Mister Exam

Factor polynomial x^2+x+6

An expression to simplify:

The solution

You have entered [src]
 2        
x  + x + 6
(x2+x)+6\left(x^{2} + x\right) + 6
x^2 + x + 6
General simplification [src]
         2
6 + x + x 
x2+x+6x^{2} + x + 6
6 + x + x^2
The perfect square
Let's highlight the perfect square of the square three-member
(x2+x)+6\left(x^{2} + x\right) + 6
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=4acb24an = \frac{4 a c - b^{2}}{4 a}
In this case
a=1a = 1
b=1b = 1
c=6c = 6
Then
m=12m = \frac{1}{2}
n=234n = \frac{23}{4}
So,
(x+12)2+234\left(x + \frac{1}{2}\right)^{2} + \frac{23}{4}
Factorization [src]
/            ____\ /            ____\
|    1   I*\/ 23 | |    1   I*\/ 23 |
|x + - + --------|*|x + - - --------|
\    2      2    / \    2      2    /
(x+(1223i2))(x+(12+23i2))\left(x + \left(\frac{1}{2} - \frac{\sqrt{23} i}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{23} i}{2}\right)\right)
(x + 1/2 + i*sqrt(23)/2)*(x + 1/2 - i*sqrt(23)/2)
Powers [src]
         2
6 + x + x 
x2+x+6x^{2} + x + 6
6 + x + x^2
Assemble expression [src]
         2
6 + x + x 
x2+x+6x^{2} + x + 6
6 + x + x^2
Combinatorics [src]
         2
6 + x + x 
x2+x+6x^{2} + x + 6
6 + x + x^2
Rational denominator [src]
         2
6 + x + x 
x2+x+6x^{2} + x + 6
6 + x + x^2
Common denominator [src]
         2
6 + x + x 
x2+x+6x^{2} + x + 6
6 + x + x^2
Numerical answer [src]
6.0 + x + x^2
6.0 + x + x^2
Trigonometric part [src]
         2
6 + x + x 
x2+x+6x^{2} + x + 6
6 + x + x^2
Combining rational expressions [src]
6 + x*(1 + x)
x(x+1)+6x \left(x + 1\right) + 6
6 + x*(1 + x)