Mathematics · Polynomial Functions · Topic 7 · 7 of 18
Remainder and Factor Theorems
Evaluate remainders efficiently and test possible factors.
Remainder TheoremThe remainder when P(x) is divided by x−c equals P(c).
Factor Theoremx−c is a factor exactly when P(c)=0.
ConnectionA zero remainder proves both a root and a factor.
Worked example
P(x)=x³−4x²+x+6; P(2)=0
Therefore x−2 is a factor of P(x).