Question

Let $g(x)=x^6+ax^5+bx^4+cx^3+dx^2+ex+y$ be a polynomial such that $g(1)=1; g(2)=2; g(3)=3; g(4)=4; g(5)=5; g(6)=6$. Then find $g(7)=?$

Answer 1

Answer:

Your Answer is 10..

Step-by-step explanation:

Since 

f(x)−x is a polynomial of degree 6 and 

has 6 roots1,2,3,4,5,6 by condition, 

we can factorize f(x)−x as:

f(x)−x=C(x−1)(x−2)(x−3)(x−4)(x−5)(x−6).

Plug in x=0 in the above expression, 

we have 3−0=C×6!, hence C=36!. 

Therefore,

f(7)=7+(f(7)−7)=7+36!(7−1)(7−2)(7−3)(7−4)(7−5)(7−6)=7+36!×6!

=10.

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