Question

Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial? Create a sample problem that has a binomial which IS a factor of the polynomial being divided, and another problem that has a binomial which is NOT a factor of the polynomial being divided.

Answer 1

first one
Create a sample problem that has a binomial which IS a factor of the polynomial being divided,

start with your polynomial in factored for, make up anything where one is a "binomial" say
(x2+2x+1)(x−4)
multiply out, and then you will be sure that x−4 is a factor of your result

Answer 2

for the second one, you can take your answer for the first one and add some number to it. then you can be sure that x−4 is not a factor