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.

Question

anonymous · Answer

Wouldn't we be looking for it to have zero remainder after we divided the binomial out? If there was a remainder then the binomial isn't a factor.

anonymous · Answer

As for coming up with a question, I'd probably just take any binomial and square it.  That way you KNOW you can divide it back out with no problem.

anonymous · Answer

$$\frac{ 2x+2 }{ x+1 } = \frac{ 2(x+1 }{ x+1 }$$
so in the end u factor out a a 2 on the top since the x+1 cancels out

anonymous · Answer

does that make sense to you ?

anonymous · Answer

For the last part of the question, about constructing a polynomial division problem that doesn't evenly divide out, I'd probably just take my trust (x+1)^2 and just add something to it at the end.  For instance, we know the (x+1) divides x^2 + 2x +1, but if we want to "break" it then I would just go with x^2 + 2x + 2.