Let f ( x ) = a 0 + a 1 x + a 2...

Amber Quinn

Amber Quinn

Answered

2022-06-27

Let f ( x ) = a 0 + a 1 x + a 2 x 2 . . . . + a n x n , where a i are non-negative integers for i = 0 , 1 , 2 , . . . . , n. If f ( 1 ) = 21 and f ( 25 ) = 78357, find the value of f ( 10 ) + 3 100

Answer & Explanation

America Barrera

America Barrera

Expert

2022-06-28Added 23 answers

Following the hint in the comment, noting that 25 3 < 78357 < 25 4 shows that n 3, i.e. f ( x ) = a 0 + a 1 x + a 2 x 2 + a 3 x 3
From here, just do long division to find a 3 , a 2 , a 1 , a 0 . For instance, 78357 = 25 3 5 + 232
, and the remainder 232 is 232 = 25 2 0 + 25 9 + 7

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