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:


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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