What is the remainder when $6 x^{2} - 4 x + 2$ is divided by $(x - 1)$ ?

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Solution

Given $f (x)$ = $6 x^{2} - 4 x + 2$ .....(I)
To find the remainder when it is divided by $(x - 1)$ , we use remainder theorem.

Remainder of $\frac{f (x)}{(x - a)}$ is $f (a)$ .
Putting value of x equal to 1 in equation (i) we get,

$f (1) = 6 (1^{2}) - 4 (1) + 2$
= 6 - 4 + 2
= 8 - 4
= 4
$\Rightarrow$ The remainder when $6 x^{2} - 4 x + 2$ is divided by $(x - 1)$ is 4.

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