Factor theorem
Let P(x) be a polynomial

Prove that
a.)If P(c)= 0 then x-c is a factor of P(x)
b.) If x-c is a factor of P(x then P(c)= 0

Question

Factor theorem  
Let P(x) be a polynomial 

Prove that
a.)If P(c)= 0 then x-c is a factor of P(x) 
b.) If x-c is a factor of P(x then P(c)= 0

anonymous · Answer

@dumbcow  pls help

dumbcow · Answer

hmm not sure how to about the formal proof...since P(c) = 0 , c is a zero thus (x-c) is factor of P(x)

dumbcow · Answer

you may want to try tagging someone else on this one...i plead to common sense but that doesn't work in mathematics :)

debbieg · Answer

Can you use the remainder theorem?

If you divide a degree n polynomial P(x) by (x-c), you get:

P(x)=(x-c)*Q(x)+r   

where the remainder r is a constant, and Q(x) is a polynomial of degree n-1.

If you can use that, then (1) should follow pretty easily when you assume that P(c)=0 (just show that the remainder in the division by x-c=0, then that means that x-c is a factor).