Question

determine the max number of real zeros that p(x)=-6x^6+7x^5-4x^4+3x^2+9x-47 has

Answer 1

Real zeros can be found by using P over Q.
Factors of P over factors of Q.

You are very fortunate to have 47 as your P as its factors are only 1 and 47. As for Q, which is 6, its factors are 1,2,3,and 6. Do remember to put plus minus in front of each P divided by Q.

Use synthetic division for a problem such as this!

Answer 2

for synthetic division how do i know what to divide p(x)=-6x^6+7x^5-4x^4+3x^2+9x-47 by?

Answer 3

you're going to divide that long equation by the quotients you got from p/q.

you will have to keep trying until you get a remainder equal to 0. Also, when setting up the synthetic division, make sure you write +0x^3 between 4x^4 and 3x^2.