Which of the following numbers cannot be a root of the polynomial function f(x)=16x7+ax3+b , where a and b are integers?

Question

Which of the following numbers cannot be a root of the polynomial function f(x)=16x⁷+ax³+b , where a and b are integers? please explain

a) 4

b) 16

c) 17

d) 12

Answer 1

When we are trying to pick factors of a polynomial our choices are all the factors of the product of the first and last term. Since b(the last term is an integer) there is no 16 x b which will have 17 as a factor so b cannot be a root

Answer 2

The piece of information critical to the answer of this problem is this:

Let P(x) be a polynomial with leading constant a_n and constant term a₀.

If c/d is a rational root of P where c and d are integers and c/d is in lowest terms, then c must divide a₀ and d must divide a_n.

I will leave to you the answer to this question.