Factor Theorem (Edexcel A-Level Mathematics): Flashcards

If $f(x)$ is divided by $(x-a)$, the remainder is $f(a)$

If $f(a) = 0$, then $(x-a)$ is a factor of $f(x)$

The remainder

$(x-a)$ is a factor of $f(x)$

Set $3x-2=0$, find $x$, evaluate $f(x)$ at that value

Use Remainder Theorem (evaluate $f(a)$)

Perform polynomial division to find other factors

Check if $f(a) = 0$

Break polynomial into all linear factors

Use Factor Theorem to create simultaneous equations

$f(-3) = 0$

When only asked for the remainder