Question

Help please: 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

If, after your division, the remainder is zero, the binomial is a factor of the polynomial. If you have a non-zero remainder, it is not.

Answer 2

suppose the binomial (ax+b) totally divides the polynimial, then the value of x for which ax+b=0, is also a zero of the polynomial. so check if -b/a is a xero of the polynomial. if yes then it is.