Question

prove that every odd polynomial function is zero at x=0

Answer 1

f(0)=-f(-0)
2 f(0)=0
f(0)=0

Answer 2

thank you
can you also help me with this question
prove that every odd polynomial P(x) is divisible by x

Answer 3

wait where did you get 2 f(0) =0 from in the above question?

Answer 4

Remainder Theorem, combined with what was just proven, should prove this.

Answer 5

show me please

Answer 6

Remainder Theorem states that the remainder when a polynomial P(x) is divided by x-a is P(a).
Now, we just proved that f(0)=0 for an odd polynomial function. Also, a polynomial is divisible by another if the remainder upon dividing the first by the second is 0.
By the Remainder Theorem, the remainder when f(x) is divided by x-0 is 0. Thus, f(x) is divisible by x.