Other

Question 1

Why can’t a degree 5 polynomial just have a range of (-infinity, infinity)

Answer 1

The end behavior of a degree five polynomial looks like an S or backward S, pointing both up and down forever

Question 2

Why a degree 10 polynomial cannot have exactly 7 real roots (including repeated roots)

Answer 2

Having 7 real roots implies 3 complex roots, which violates the conjugate pair theorem

Question 3

What is the conjugate pair theorem?

Answer 3

If a+bi is a factor of your polynomial, then a-bi is also a factor