Note that the sum of coefficients of a polynomial Q(x) is equal to Q(1).
#polynomial problem
hardy crow
tame pumice
Note that the sum of coefficients of a polynomial Q(x) is equal to Q(1).
Can you please describe how? I mean is 1 is the answer?
hardy crow
No. We have:
Q(x - 1) = P(x^2 + 1)/(x^2 - 1)
What value of x should we take to get Q(1)?
tame pumice
No. We have:
Q(x - 1) = P(x^2 + 1)/(x^2 - 1)
What value of x should we take to g...
2 ?
tame pumice
So, when you substitute x = 2, what will the expression look like?
Q(1)= P(5)/3
hardy crow
Yes.
Now we need to deal with P(5).
By the statement of the problem, we have P(x + 5) = ax^n + ... + bx + 3. So, what value of x should we take here to obtain just 3?
hardy crow
Yes. So, what is P(5) equal to?
tame pumice
Yes. So, what is P(5) equal to?
P(5)=Q(1)×3
hardy crow
By the statement of the problem, we have P(x + 5) = ax^n + ... + bx + 3. So, wha...
Well, yes. But when you plug in x = 0 here, you get P(5) = 3, right?
tame pumice
Well, yes. But when you plug in x = 0 here, you get P(5) = 3, right?
Yes yes we get here P(5) = 3
hardy crow
Good.
So, if Q(1) = P(5)/3 and P(5) = 3, what is Q(1) equal to?
tame pumice
Good.
So, if Q(1) = P(5)/3 and P(5) = 3, what is Q(1) equal to?
Q(1) is equal to 1
hardy crow
Yes, very good! And that is the sum of coefficients of Q(x), as we discussed above.
So, the answer is 1.
hardy crow
You're welcome!
tame pumice
Thanks for the help ^_^