# Test for love

**Algebra**Level 3

Sandeep is in love, and on the valentine's day he had his own plans, he thought of presenting his love with another beautiful gift.

But his girlfriend strangely gave him a test, and said that only if he passes this test she will truly accept him as a lover, and the question was: "How many gifts did you present me in the until the kiss day?"

But he was not a world memory champion, so he couldn't remember the exact number. But he was clever enough to have made a polynomial that gives the number of gifts he presented until a given day, but he remembers only this:

\[p(1)=1\\p(2)=4\\p(3)=9\\p(4)=16\\p(5)=25\]

He remembers that it was a \(5^{th}\) degree polynomial with leading coefficient **2**. And we know that kiss day is the \(6^{th}\) day of the Valentine's week, so what is \(p(6)\) ?

*This is my submission for the Valentine's day celebrations, Please upvote my comment if you like it!*

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