Question

A polynomial is to be constructed that will touch the x axis at most 7 times. What is the minimum degree of the polynomial ?

Answer 1

Minimum degree
ok, so
a first degree (y=mx+b) can cross at most 1 time
a 2nd degree (y=ax²+bx+c) can cross at most 2 times

so therfor we see that a nth degree polynomial can cross or touch at most n times

so 7 times means 7th degree

minimum degree is 7th degree