Write a polynomial whose only zero is 8 with multiplicity 6. What is its degree?

Answer 1

The factor that gives you a zero of 8 is (x-8) Since it is multiplicity of 6, it would be f(x)=(x-8)⁶

If you multiply this out, the highest exponent would be 6, therefore the degree is 6.

Answer 2

The answer is simply (x-8)^{6}.

Answer 3

There's only one zero but it occurs 6 times:

P(x) = (x-8) (x-8) (x-8) (x-8) (x-8) (x-8) = (x-8)⁶

You can multiply it by any constant to get other polynomials with the same zero and multiplicity, such as P(x) = -3(x-8)⁶ or P(x) = 17(x-8)⁶. The degree is equal to the highest exponent in the polynomial.