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

P(x)
------
(ax+b)


let P(x) = (ax+b) Q(x) , therefore it has the binomial as a factor

whenever (ax+b) = 0, say at x = r

P(r) = (ar+b) Q(r)
| =0 |

P(r) = 0 as well

Answer 2

so, IF the binomial is a factor of the polynomial; then whatever zeroes out the binomial will have to zero out the polynomial as well.

Answer 3

if not, then the poly does not have the binomial as a factor.