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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