(a) If a is a zero of the polynomial P(x), then must be a factor of P(x). (b) If a is a zero of multiplicity m of the polynomial P(x), then must be a factor of P(x) when we factor P completely.

Question

(a) If a is a zero of the polynomial P(x), then 

 

 must be a factor of P(x).

(b) If a is a zero of multiplicity m of the polynomial P(x), then 

 

 must be a factor of P(x) when we factor P completely.

Answer 1

a) if a is a zero, x-a is a factor. just change the sign and stick an x in front

b) if a is a zero of multiplicity m, then (x-a)^m is a factor