Question
Use factor theorem to determine whether $x+3$ is a factor of $x^2+2 x-3$ or not.
✓
Answer
$p(x)=x^2+2 x-3$
$\text { Divisor }=x+3$
$\therefore \text { take } x=-3$
$\therefore \text { Remainder }=p(-3)$
$p(x)=x^2+2 x-3$
$\therefore p(-3)=(-3)^2+2(-3)-3$
$=9-6-3$
$\therefore p(-3)=0$
$\therefore$ By factor theorem, $x +3$ is a factor of $x ^2+2 x -3$.
$\text { Divisor }=x+3$
$\therefore \text { take } x=-3$
$\therefore \text { Remainder }=p(-3)$
$p(x)=x^2+2 x-3$
$\therefore p(-3)=(-3)^2+2(-3)-3$
$=9-6-3$
$\therefore p(-3)=0$
$\therefore$ By factor theorem, $x +3$ is a factor of $x ^2+2 x -3$.
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