Part 1: 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.

Part 2: View and comment on the work of at least 2 other students. Try to choose students’ whose examples are different from the ones you created.

Question

Part 1: 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. 

Part 2: View and comment on the work of at least 2 other students. Try to choose students’ whose examples are different from the ones you created.

anonymous · Answer

Upon dividing, you know that the binomial is a factor if you get a remainder of zero. It's the same principle behind the fact that $2$ is a factor of $4$, but not $5$, since $\dfrac{4}{2}=2$ and $\dfrac{5}{2}=2+\dfrac{1}{2}$.