Factor theorem
If a is a factor of a polynomial , then .
Remainder theorem
Instead of dividing a polynomial entirely, we can use the following equation to calculate the remainder of division by a linear polynomial:
Then the remainder is equal to .
If a (ax−b) is a factor of a polynomial P(x), then P(ab)=0.
Instead of dividing a polynomial entirely, we can use the following equation to calculate the remainder of division by a linear polynomial:
P(x)=Q(x)(ax−b)+abThen the remainder is equal to ab.