# 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:

Namesolution foundcomment
@crokkoncorrect
@zuerichcorrect

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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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### The next contest starts in 2 days. Don't miss it!

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3 comments

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

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