Find whether $x - 1$ is a factor of $2 x^{2} - 5 x + 3$ .

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Solution

Let $p (x) =$ $2 x^{2} - 5 x + 3$
By the factor theorem, $x - 1$ is a factor of $p (x)$ , if $p (1) = 0$
Find the value of $p (1)$
$p (1) = 2 x^{2} - 5 x + 3$ .........(Substitute $x = 1$ )
$p (1) = 2 (1)^{2} - 5 (1) + 3$
$0 = 2 - 5 + 3$
$0 = - 3 + 3$
$0 = 0$
Therefore, $x - 1$ is a factor of $p (x)$ .

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