Use factor theorem to verify that the following polynomial $q (x)$ is a factor of $p (x)$ :
$p (x) = 3 x^{2} - 5 x + 2, q (x) = 3 x - 2$

True

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False

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Solution

The correct option is A True
$q (x) = 3 x - 2$ $\Rightarrow$ $x = \frac{2}{3}$
$q (x)$ will be a factor of $p (x)$ , if $p (\frac{2}{3}) = 0$

So, $p (\frac{2}{3})$ $= 3 {(\frac{2}{3})}^{2} - 5 (\frac{2}{3}) + 2$

$= \frac{4}{3} - \frac{10}{3} + 2$

$= \frac{4 - 10 + 6}{3} = 0$

Therefore, by factor theorem $q (x) = 3 x - 2$ is factor of $p (x) = 3 x^{2} - 5 x + 2$ .

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(i)

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