SOLUTION: suppose you divide a polynomial by a binomial. how do you know if the binomial is a factor of the polynomial?

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Question 588876: suppose you divide a polynomial by a binomial. how do you know if the binomial is a factor of the polynomial?
Found 2 solutions by richard1234, KMST:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
If the remainder is 0.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the zero of the binomial is a zero of the polynomial, the binomial is a factor of the polynomial.
For example, x-1 is a factor of
P%28x%29=57x%5E7-23x%5E6%2B48x%5E5-76x%5E4%2B11x%5E3-15x%5E2%2B4x-6 because
x=1 is the zero of x-1 and
P%281%29=57-23%2B48-76%2B11-15%2B4-6=0