# Math Contest #23 Results and Solution

## Solution

The problem of this contest was to solve a polynomial:

`x⁴ + 8x³ + 24x² + 32x + 15 = 0`

This might look pretty hard, but if you know what to look for you might notice a regularity there.

First of all you need to add 1:

`x⁴ + 8x³ + 24x² + 32x + 16 = 1`

And now the magic happens when you remove the factors typical for to the binomial theorem:

`x⁴ + 4*2x³ + 6*4x² + 4*8x + 16 = 1`

`x⁴ + 4*2¹x³ + 6*2²x² + 4*2³x + 2⁴ = 1`

According to the binomial theorem that is equal to:

`(x+2)⁴ = 1`

taking the 4th root leads to the four solutions:

`x₁+2 = 1 → x₁ = -1`

,

`x₂+2 = -1 → x₂ = -3`

,

`x₃+2 = i → x₃ = i-2`

,

`x₄+2 = -i → x₄ = -i-2`

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### List of participants with their entries:

Name | solution found | comment |
---|---|---|

@crokkon | correct | |

@zuerich | correct |

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## Winner draw:

Not necessary since the reward can be divided be the number of entries:

Congratulations @zuerich and @crokkon , you won 1 SBI each!

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woah this way to solve it is relly cool. Math impresses me every time I learn something new

thanks :)

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