Question

$x$	$f\left(x\right)$
$0$	$3$
$2$	$1$
$4$	$0$
$5$	$-2$

The function $f$ is defined by a polynomial. Some values of $x$ and $f\left(x\right)$ are shown in the table above. Which of the following must be a factor of $f\left(x\right)$?

• A. $x-2$
• B. $x-0$
• C. $x-4$
• D. $x-5$

Answer 1

Answer: (C)

$x-4$

$(x-\alpha )$ will be a factor of $f\left(x\right)$ if for $x=\alpha ,f\left(x\right)=0$ or $f\left(\alpha \right)=0$
From the given table, At $x=4,f\left(x\right)=0$
$\Rightarrow f\left(4\right)=0$
$\therefore 4$ is zero of $f\left(x\right)$
$\Rightarrow (x-4)$ is a factor of $f\left(x\right)$