Maths - Factor Theorem
Pearson Edexcel Mathematics 2022
Flashcards
The factor theorem
If $f(x)$ is a polynomial and $f(p) = 0$, what must be true?
$(x - p)$ is a factor of $f(x)$.
If $f(x)$ is a polynomial and $(x-p)$ is a factor of $f(x)$, what must be true?
\[f(p) = 0\]
The remainder theorem
If $f(x)$ is a polynomial and $f\left(\frac{b}{a}\right) = r$, what must be true?
Dividing $f(x)$ by $(ax - b)$ has remainder $r$.
If $f(x)$ is a polynomial and dividing by $(ax - b)$ has remainder $r$, what must be true?
\[f\left(\frac{b}{a}\right) = r\]